manoranjan kumar | S. N. Bose National Centre for Basic Sciences (original) (raw)

Papers by manoranjan kumar

Condensed Matter

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferro... more Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs c...

arXiv (Cornell University), Jul 8, 2019

The spin-Peierls transition is modeled in the dimer phase of the spin-1/2 chain with exchanges J1... more The spin-Peierls transition is modeled in the dimer phase of the spin-1/2 chain with exchanges J1, J2 = αJ1 between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization δ(T) compared to Peierls systems with nondegenerate ground states. The parameters J1 = 160 K, α = 0.35 plus a lattice stiffness account for the magnetic susceptibility of CuGeO3, its specific heat anomaly, and the T dependence of the lowest gap.

arXiv (Cornell University), May 15, 2019

Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quan... more Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quantum cell models at high temperature T. Density matrix renormalization group (DMRG) calculations of progressively larger systems are used to obtain excitations up to a cutoff WC and the low-T thermodynamics. The hybrid approach is applied to the magnetic susceptibility χ(T) and specific heat C(T) of spin-1/2 chains with isotropic exchange such as the linear Heisenberg antiferromagnet (HAF) and the frustrated J1 − J2 model with ferromagnetic (F) J1 < 0 and antiferromagnetic (AF) J2 > 0. The hybrid approach is fully validated by comparison with HAF results. It extends J1 − J2 thermodynamics down to T ∼ 0.01|J1| for J2/|J1| ≥ αc = 1/4 and is consistent with other methods. The criterion for the cutoff WC (N) in systems of N spins is discussed. The cutoff leads to bounds for the thermodynamic limit that are best satisfied at a specific T (N) at system size N .

Journal of Applied Physics

We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems ... more We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for J1 ≥ 1.82; the gs spin corresponds to ferromagnetic alignment of effective S = 2 objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning J1 in a finite size system. The switching pattern is nonmonotonic as a function of J1, and depends on the system size. It appears to be the consequence of higher J1 favoring higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin parity and mirror symmetry breaking giving rise to spin current in the gs of the system.

Physical Review B

The spin−1/2 chain with ferromagnetic exchange J1 < 0 between first neighbors and antiferromagnet... more The spin−1/2 chain with ferromagnetic exchange J1 < 0 between first neighbors and antiferromagnetic J2 > 0 between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration α = J2/|J1|. Instead of chain dimerization with two spins per unit cell, J1 − J2 models with α > 0.65 and linear spin-phonon coupling are unconditionally unstable to sublattice dimerization with four spins per unit cell. Unequal J1 to neighbors to the right and left extends the model to gapped (γ > 0) chains with conditional SP transitions at TSP to dimerized sublattices and a weaker specific heat C(T) anomaly. The spin susceptibility χ(T) and C(T) are obtained in the thermodynamic limit by a combination of exact diagonalization of small systems with α > 0.65 and density matrix renormalization group (DMRG) calculations of systems up to N ∼ 100 spins. Both J1 − J2 and γ > 0 models account quantitatively for χ(T) and C(T) in the paramagnetic phase of β-TeVO4 for T > 8 K, but lower T indicates a gapped chain instead of a J1 − J2 model as previously thought. The same parameters and TSP = 4.6 K generate a C(T)/T anomaly that reproduces the anomaly at the 4.6 K transition of β-TeVO4, but not the weak χ(T) signature. I.

Physical Review B, 2021

The antiferromagnetic J1 − J2 model is a spin-1/2 chain with isotropic exchange J1 > 0 between fi... more The antiferromagnetic J1 − J2 model is a spin-1/2 chain with isotropic exchange J1 > 0 between first neighbors and J2 = αJ1 between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with ∆(α) > 0 and doubly degenerate ground states. Exact thermodynamics is limited to α = 0, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration α followed by density matrix renormalization group (DMRG) calculations returns the entropy density S(T, α, N) and magnetic susceptibility χ(T, α, N) of progressively larger systems up to N = 96 or 152 spins. Convergence to the thermodynamics limit, S(T, α) or χ(T, α), is demonstrated down to T /J ∼ 0.01 in the sectors α < 1 and α > 1. S(T, α) yields the critical points between gapless phases with S (0, α) > 0 and gapped phases with S (0, α) = 0. The S (T, α) maximum at T * (α) is obtained directly in chains with large ∆(α) and by extrapolation for small gaps. A phenomenological approximation for S(T, α) down to T = 0 indicates power-law deviations T −γ(α) from exp(−∆(α)/T) with exponent γ(α) that increases with α. The χ(T, α) analysis also yields power-law deviations, but with exponent η(α) that decreases with α. S(T, α) and the spin density ρ(T, α) = 4T χ(T, α) probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant S(T, α)/ρ(T, α) for T < 0.10. Remarkably, the ratio decreases (increases) with T in chains with large (small) ∆(α). I.

arXiv: Strongly Correlated Electrons, 2016

The density matrix renormalization group (DMRG) method generates the low-energy states of linear ... more The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of NNN sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin Sge1S \ge 1Sge1 and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.

Physical Review B, 2021

The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and sevenme... more The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and sevenmembered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (J2 = 1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J1) along the rungs. As a function of J1, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of diverse gs properties such as spin gap, spin-spin correlations, spin density and bond order reveal that the system has four distinct phases, namely, the AF phase at small J1; the ferrimagnetic phase with gs spin SG = n for 1.44 < J1 < 4.74 and with SG = 2n for J1 > 5.63, where n is the number of unit cells; and a reentrant nonmagnetic phase at 4.74 < J1 < 5.44. The system also shows the presence of spin current at specific J1 values due to simultaneous breaking of both reflection and spin parity symmetries.

Journal of Magnetism and Magnetic Materials, 2021

The spin-1/2 chain with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neigh... more The spin-1/2 chain with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neighbors, respectively, has both gapless and gapped (∆(α) > 0) quantum phases at frustration 0 ≤ α ≤ 3/4. The ground state instability of regular (δ = 0) chains to dimerization (δ > 0) drives a spin-Peierls transition at TSP (α) that varies with α in these strongly correlated systems. The thermodynamic limit of correlated states is obtained by exact treatment of short chains followed by density matrix renormalization calculations of progressively longer chains. The doubly degenerate ground states of the gapped regular phase are bond order waves (BOWs) with long-range bondbond correlations and electronic dimerization δe(α). The T dependence of δe(T, α) is found using four-spin correlation functions and contrasted to structural dimerization δ(T, α) at T ≤ TSP (α). The relation between TSP (α) and the T = 0 gap ∆(δ(0), α) varies with frustration in both gapless and gapped phases. The magnetic susceptibility χ(T, α) at T > TSP can be used to identify physical realizations of spin-Peierls systems. The α = 1/2 chain illustrates the characteristic BOW features of a regular chain with a large singlet-triplet gap and electronic dimerization.

Physical Review B, 2020

The spin-Peierls transition at TSP of spin-1/2 chains with isotropic exchange interactions has pr... more The spin-Peierls transition at TSP of spin-1/2 chains with isotropic exchange interactions has previously been modeled as correlated for T > TSP and mean field for T < TSP. We use correlated states throughout in the J1 − J2 model with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neighbors, respectively, and variable frustration 0 ≤ α ≤ 0.50. The thermodynamic limit is reached at high T by exact diagonalization of short chains and at low T by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter TSP yields both the stiffness and the lattice dimerization δ(T). The relation between TSP and ∆(δ, α), the T = 0 gap induced by dimerization, depends strongly on α and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS4C4(CF3)4 crystals (J1 = 79 K, α = 0, TSP = 12 K) and CuGeO3 crystals (J1 = 160 K, α = 0.35, TSP = 14 K). The same parameters describe the specific heat anomaly of CuGeO3 and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that δ(0) limits the range of spin correlations at T = 0 while T > 0 limits the range at δ = 0.

Physical Review B, 2019

We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two J1 −... more We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two J1 − J2 zigzag ladders interacting through anti-ferromagnetic rung coupling J3. The J1 and J2 are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group (DMRG) method and linearized spin wave analysis. In small J2 limit a short range striped collinear phase is found in the presence of J3, whereas, in the large J2/J3 limit non-collinear quasi-long range phase is found. The system shows a short range non-collinear state in large J3 limit. The short range order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin wave analysis show similar phase boundary between collinear striped and non-collinear short range phases, and the collinear phase region shrinks with increasing J3. We apply this model to understand the magnetic properties of CaV2O5 and also fit the experimental data of susceptibility and magnetization. We note that J3 is a dominant interaction in this material, whereas J1 and J2 are approximately half of J3. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

Physical Review B, 2018

The magnetic susceptibility χ(T) of spin-1/2 chains is widely used to quantify exchange interacti... more The magnetic susceptibility χ(T) of spin-1/2 chains is widely used to quantify exchange interactions, even though χ(T) is similar for different combinations of ferromagnetic J1 between first neighbors and antiferromagnetic J2 between second neighbors. We point out that the spin specific heat C(T) directly determines the ratio α = J2/|J1| of competing interactions. The J1 − J2 model is used to fit the isothermal magnetization M (T, H) and C(T, H) of spin-1/2 Cu(II) chains in LiCuSbO4. By fixing α, C(T) resolves the offsetting J1, α combinations obtained from M (T, H) in cuprates with frustrated spin chains.

Physical Review B, 2017

The J1 − J2 spin chain model with nearest neighbor J1 and next nearest neighbor antiferromagnetic... more The J1 − J2 spin chain model with nearest neighbor J1 and next nearest neighbor antiferromagnetic J2 interaction is one of the most popular frustrated magnetic models. This model system has been extensively studied theoretically and applied to explain the magnetic properties of the real low-dimensional materials. However, existence of different phases for the J1 − J2 model in an axial magnetic field h is either not understood or has been controversial. In this paper we show the existence of higher order p > 4 multipolar phase near the critical point (J2/J1)c = −0.25. The criterion to detect the quadrupolar or spin nematic (SN)/spin density wave of type two (SDW2) phase using the inelastic neutron scattering (INS) experiment data is also discussed, and INS data of LiCuVO4 compound is modelled. We discuss the dimerized and degenerate ground state in the quadrupolar phase. The major contribution of binding energy in the spin-1/2 system comes from the longitudinal component of the nearest neighbor bonds. We also study spin nematic/SDW2 phase in spin-1 system in large J2/J1 limit.

Physical Review B, 2017

The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonali... more The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange J2 > 0 between first neighbors in the legs, variable isotropic AF exchange J1 between some first neighbors in different legs, and an unpaired spin per odd-membered ring when J1 J2. Ladders with skewed rungs and variable J1 have frustrated AF interactions leading to multiple quantum phases: AF at small J1, either F or AF at large J1, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate J1.

Journal of Magnetism and Magnetic Materials, 2018

Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg ar... more Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings J 1. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with J 2 1 , and the systems show an incommensurate phase for 0.0 < J 1 < 1.0. The spin-spin correlation functions in the incommensurate phase follow power law decay which is very similar to Heisenberg antiferromagnetic chain in external magnetic field. In large J 1 limit, the normal ladder behaves like a collection of singlet dimers, whereas the zigzag ladder behaves as a one dimensional spin-1/2 antiferromagnetic chain.

Physical Review B, 2016

Linear Heisenberg antiferromagnets (HAFs) are chains of spinS sites with isotropic exchange J bet... more Linear Heisenberg antiferromagnets (HAFs) are chains of spinS sites with isotropic exchange J between neighbors. Open and periodic boundary conditions return the same ground state energy per site in the thermodynamic limit, but not the same spin SG when S ≥ 1. The ground state of open chains of N spins has SG = 0 or S, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities ρ(r, N) of edge states in HAFs with S = 1, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with ρ(r, N) ∝ (−1) r−1 for r = 1, 2,. .. N. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy Γ(N) that decreases exponentially with N for integer S and faster than 1/N for half integer S. The spin densities and excitation energy are quantitatively modeled for integer S chains longer than 5ξ spins by two parameters, the correlation length ξ and the SDW amplitude, with ξ = 6.048 for S = 1 and 49.0 for S = 2. The BI-SDWs of S = 3/2 chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases |Γ(N)| and weakens the size dependence. The nonlinear sigma model (NLσM) has been applied the HAFs, primarily to S = 1 with even N , to discuss spin densities and exchange between localized states at the ends as Γ(N) ∝ (−1) N exp(−N/ξ). S = 1 chains with odd N are fully consistent with the NLσM; S = 2 chains have two gaps Γ(N) with the same ξ as predicted whose ratio is 3.45 rather than 3; the NLσM is more approximate for S = 3/2 chains with even N and is modified for exchange between ends for odd N .

Physical Review B, 2016

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y-... more An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y-junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 ≈ 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in halffilled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA = NB. The ground state (GS) and spin densities ρr =< S z r > at site r are quite different for junctions with S = 1/2, 1, 3/2 and 2. The GS has finite total spin SG = 2S(S) for even (odd) N and for MG = SG in the SG spin manifold, ρr > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized Sz = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave (SDW) with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Physica B: Condensed Matter, 2010

The bond order wave (BOW) phase of half-filled linear Hubbard-type models is narrow and difficult... more The bond order wave (BOW) phase of half-filled linear Hubbard-type models is narrow and difficult to characterize aside from a few ground state properties. The BOW phase of a frustrated Heisenberg spin chain is wide and tractable. It has broken inversion symmetry C i in a regular array and finite gap E m to the lowest triplet state. The spin-BOW is exact in finite systems at a special point. Its elementary excitations are spin-1/2 solitons that connect BOWs with opposite phase. The same patterns of spin densities and bond orders appear in the BOW phase of Hubbard-type models. Infrared (IR) active lattice phonons or molecular vibrations are derivatives of P, the polarization along the stack. Molecular vibrations that are forbidden in regular arrays become IR active when C i symmetry is broken. 1:1 alkali-TCNQ salts contain half-filled regular TCNQstacks at high temperature, down to 100 K in the Rb-TCNQ(II) polymorph whose magnetic susceptibility and polarized IR spectra indicate a BOW phase. More complete modeling will require explicit electronic coupling to phonons and molecular vibrations.

Physical Review B, 2010

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J1, J2 between first and second nei... more The linear spin-1/2 Heisenberg antiferromagnet with exchanges J1, J2 between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J2/J1 = 0.2411 and is particularly simple at J2/J1 = 1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry and a finite energy gap Em to the lowest triplet state. The interval 0.4 < J2/J1 < 1.0 has large Em and small finite size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large Em are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility χM (T) is exponentially small for T ≪ Em and increases nearly linearly with T to a broad maximum. J1, J2 spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-TCNQ salts.

Condensed Matter

Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferro... more Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs c...

arXiv (Cornell University), Jul 8, 2019

The spin-Peierls transition is modeled in the dimer phase of the spin-1/2 chain with exchanges J1... more The spin-Peierls transition is modeled in the dimer phase of the spin-1/2 chain with exchanges J1, J2 = αJ1 between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization δ(T) compared to Peierls systems with nondegenerate ground states. The parameters J1 = 160 K, α = 0.35 plus a lattice stiffness account for the magnetic susceptibility of CuGeO3, its specific heat anomaly, and the T dependence of the lowest gap.

arXiv (Cornell University), May 15, 2019

Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quan... more Exact diagonalization (ED) of small model systems gives the thermodynamics of spin chains or quantum cell models at high temperature T. Density matrix renormalization group (DMRG) calculations of progressively larger systems are used to obtain excitations up to a cutoff WC and the low-T thermodynamics. The hybrid approach is applied to the magnetic susceptibility χ(T) and specific heat C(T) of spin-1/2 chains with isotropic exchange such as the linear Heisenberg antiferromagnet (HAF) and the frustrated J1 − J2 model with ferromagnetic (F) J1 < 0 and antiferromagnetic (AF) J2 > 0. The hybrid approach is fully validated by comparison with HAF results. It extends J1 − J2 thermodynamics down to T ∼ 0.01|J1| for J2/|J1| ≥ αc = 1/4 and is consistent with other methods. The criterion for the cutoff WC (N) in systems of N spins is discussed. The cutoff leads to bounds for the thermodynamic limit that are best satisfied at a specific T (N) at system size N .

Journal of Applied Physics

We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems ... more We study the quantum phase transitions of frustrated antiferromagnetic Heisenberg spin-1 systems on the 3/4 and 3/5 skewed two leg ladder geometries. These systems can be viewed as arising by periodically removing rung bonds from a zigzag ladder. We find that in large systems, the ground state (gs) of the 3/4 ladder switches from a singlet to a magnetic state for J1 ≥ 1.82; the gs spin corresponds to ferromagnetic alignment of effective S = 2 objects on each unit cell. The gs of antiferromagnetic exchange Heisenberg spin-1 system on a 3/5 skewed ladder is highly frustrated and has spiral spin arrangements. The amplitude of the spin density wave in the 3/5 ladder is significantly larger compared to that in the magnetic state of the 3/4 ladder. The gs of the system switches between singlet state and low spin magnetic states multiple times on tuning J1 in a finite size system. The switching pattern is nonmonotonic as a function of J1, and depends on the system size. It appears to be the consequence of higher J1 favoring higher spin magnetic state and the finite system favoring a standing spin wave. For some specific parameter values, the magnetic gs in the 3/5 system is doubly degenerate in two different mirror symmetry subspaces. This degeneracy leads to spontaneous spin parity and mirror symmetry breaking giving rise to spin current in the gs of the system.

Physical Review B

The spin−1/2 chain with ferromagnetic exchange J1 < 0 between first neighbors and antiferromagnet... more The spin−1/2 chain with ferromagnetic exchange J1 < 0 between first neighbors and antiferromagnetic J2 > 0 between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration α = J2/|J1|. Instead of chain dimerization with two spins per unit cell, J1 − J2 models with α > 0.65 and linear spin-phonon coupling are unconditionally unstable to sublattice dimerization with four spins per unit cell. Unequal J1 to neighbors to the right and left extends the model to gapped (γ > 0) chains with conditional SP transitions at TSP to dimerized sublattices and a weaker specific heat C(T) anomaly. The spin susceptibility χ(T) and C(T) are obtained in the thermodynamic limit by a combination of exact diagonalization of small systems with α > 0.65 and density matrix renormalization group (DMRG) calculations of systems up to N ∼ 100 spins. Both J1 − J2 and γ > 0 models account quantitatively for χ(T) and C(T) in the paramagnetic phase of β-TeVO4 for T > 8 K, but lower T indicates a gapped chain instead of a J1 − J2 model as previously thought. The same parameters and TSP = 4.6 K generate a C(T)/T anomaly that reproduces the anomaly at the 4.6 K transition of β-TeVO4, but not the weak χ(T) signature. I.

Physical Review B, 2021

The antiferromagnetic J1 − J2 model is a spin-1/2 chain with isotropic exchange J1 > 0 between fi... more The antiferromagnetic J1 − J2 model is a spin-1/2 chain with isotropic exchange J1 > 0 between first neighbors and J2 = αJ1 between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with ∆(α) > 0 and doubly degenerate ground states. Exact thermodynamics is limited to α = 0, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration α followed by density matrix renormalization group (DMRG) calculations returns the entropy density S(T, α, N) and magnetic susceptibility χ(T, α, N) of progressively larger systems up to N = 96 or 152 spins. Convergence to the thermodynamics limit, S(T, α) or χ(T, α), is demonstrated down to T /J ∼ 0.01 in the sectors α < 1 and α > 1. S(T, α) yields the critical points between gapless phases with S (0, α) > 0 and gapped phases with S (0, α) = 0. The S (T, α) maximum at T * (α) is obtained directly in chains with large ∆(α) and by extrapolation for small gaps. A phenomenological approximation for S(T, α) down to T = 0 indicates power-law deviations T −γ(α) from exp(−∆(α)/T) with exponent γ(α) that increases with α. The χ(T, α) analysis also yields power-law deviations, but with exponent η(α) that decreases with α. S(T, α) and the spin density ρ(T, α) = 4T χ(T, α) probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant S(T, α)/ρ(T, α) for T < 0.10. Remarkably, the ratio decreases (increases) with T in chains with large (small) ∆(α). I.

arXiv: Strongly Correlated Electrons, 2016

The density matrix renormalization group (DMRG) method generates the low-energy states of linear ... more The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of NNN sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin Sge1S \ge 1Sge1 and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.

Physical Review B, 2021

The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and sevenme... more The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and sevenmembered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (J2 = 1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J1) along the rungs. As a function of J1, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of diverse gs properties such as spin gap, spin-spin correlations, spin density and bond order reveal that the system has four distinct phases, namely, the AF phase at small J1; the ferrimagnetic phase with gs spin SG = n for 1.44 < J1 < 4.74 and with SG = 2n for J1 > 5.63, where n is the number of unit cells; and a reentrant nonmagnetic phase at 4.74 < J1 < 5.44. The system also shows the presence of spin current at specific J1 values due to simultaneous breaking of both reflection and spin parity symmetries.

Journal of Magnetism and Magnetic Materials, 2021

The spin-1/2 chain with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neigh... more The spin-1/2 chain with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neighbors, respectively, has both gapless and gapped (∆(α) > 0) quantum phases at frustration 0 ≤ α ≤ 3/4. The ground state instability of regular (δ = 0) chains to dimerization (δ > 0) drives a spin-Peierls transition at TSP (α) that varies with α in these strongly correlated systems. The thermodynamic limit of correlated states is obtained by exact treatment of short chains followed by density matrix renormalization calculations of progressively longer chains. The doubly degenerate ground states of the gapped regular phase are bond order waves (BOWs) with long-range bondbond correlations and electronic dimerization δe(α). The T dependence of δe(T, α) is found using four-spin correlation functions and contrasted to structural dimerization δ(T, α) at T ≤ TSP (α). The relation between TSP (α) and the T = 0 gap ∆(δ(0), α) varies with frustration in both gapless and gapped phases. The magnetic susceptibility χ(T, α) at T > TSP can be used to identify physical realizations of spin-Peierls systems. The α = 1/2 chain illustrates the characteristic BOW features of a regular chain with a large singlet-triplet gap and electronic dimerization.

Physical Review B, 2020

The spin-Peierls transition at TSP of spin-1/2 chains with isotropic exchange interactions has pr... more The spin-Peierls transition at TSP of spin-1/2 chains with isotropic exchange interactions has previously been modeled as correlated for T > TSP and mean field for T < TSP. We use correlated states throughout in the J1 − J2 model with antiferromagnetic exchange J1 and J2 = αJ1 between first and second neighbors, respectively, and variable frustration 0 ≤ α ≤ 0.50. The thermodynamic limit is reached at high T by exact diagonalization of short chains and at low T by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter TSP yields both the stiffness and the lattice dimerization δ(T). The relation between TSP and ∆(δ, α), the T = 0 gap induced by dimerization, depends strongly on α and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS4C4(CF3)4 crystals (J1 = 79 K, α = 0, TSP = 12 K) and CuGeO3 crystals (J1 = 160 K, α = 0.35, TSP = 14 K). The same parameters describe the specific heat anomaly of CuGeO3 and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that δ(0) limits the range of spin correlations at T = 0 while T > 0 limits the range at δ = 0.

Physical Review B, 2019

We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two J1 −... more We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two J1 − J2 zigzag ladders interacting through anti-ferromagnetic rung coupling J3. The J1 and J2 are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group (DMRG) method and linearized spin wave analysis. In small J2 limit a short range striped collinear phase is found in the presence of J3, whereas, in the large J2/J3 limit non-collinear quasi-long range phase is found. The system shows a short range non-collinear state in large J3 limit. The short range order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin wave analysis show similar phase boundary between collinear striped and non-collinear short range phases, and the collinear phase region shrinks with increasing J3. We apply this model to understand the magnetic properties of CaV2O5 and also fit the experimental data of susceptibility and magnetization. We note that J3 is a dominant interaction in this material, whereas J1 and J2 are approximately half of J3. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

Physical Review B, 2018

The magnetic susceptibility χ(T) of spin-1/2 chains is widely used to quantify exchange interacti... more The magnetic susceptibility χ(T) of spin-1/2 chains is widely used to quantify exchange interactions, even though χ(T) is similar for different combinations of ferromagnetic J1 between first neighbors and antiferromagnetic J2 between second neighbors. We point out that the spin specific heat C(T) directly determines the ratio α = J2/|J1| of competing interactions. The J1 − J2 model is used to fit the isothermal magnetization M (T, H) and C(T, H) of spin-1/2 Cu(II) chains in LiCuSbO4. By fixing α, C(T) resolves the offsetting J1, α combinations obtained from M (T, H) in cuprates with frustrated spin chains.

Physical Review B, 2017

The J1 − J2 spin chain model with nearest neighbor J1 and next nearest neighbor antiferromagnetic... more The J1 − J2 spin chain model with nearest neighbor J1 and next nearest neighbor antiferromagnetic J2 interaction is one of the most popular frustrated magnetic models. This model system has been extensively studied theoretically and applied to explain the magnetic properties of the real low-dimensional materials. However, existence of different phases for the J1 − J2 model in an axial magnetic field h is either not understood or has been controversial. In this paper we show the existence of higher order p > 4 multipolar phase near the critical point (J2/J1)c = −0.25. The criterion to detect the quadrupolar or spin nematic (SN)/spin density wave of type two (SDW2) phase using the inelastic neutron scattering (INS) experiment data is also discussed, and INS data of LiCuVO4 compound is modelled. We discuss the dimerized and degenerate ground state in the quadrupolar phase. The major contribution of binding energy in the spin-1/2 system comes from the longitudinal component of the nearest neighbor bonds. We also study spin nematic/SDW2 phase in spin-1 system in large J2/J1 limit.

Physical Review B, 2017

The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonali... more The quantum phases of 2-leg spin-1/2 ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density matrix renormalization group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange J2 > 0 between first neighbors in the legs, variable isotropic AF exchange J1 between some first neighbors in different legs, and an unpaired spin per odd-membered ring when J1 J2. Ladders with skewed rungs and variable J1 have frustrated AF interactions leading to multiple quantum phases: AF at small J1, either F or AF at large J1, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate J1.

Journal of Magnetism and Magnetic Materials, 2018

Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg ar... more Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings J 1. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with J 2 1 , and the systems show an incommensurate phase for 0.0 < J 1 < 1.0. The spin-spin correlation functions in the incommensurate phase follow power law decay which is very similar to Heisenberg antiferromagnetic chain in external magnetic field. In large J 1 limit, the normal ladder behaves like a collection of singlet dimers, whereas the zigzag ladder behaves as a one dimensional spin-1/2 antiferromagnetic chain.

Physical Review B, 2016

Linear Heisenberg antiferromagnets (HAFs) are chains of spinS sites with isotropic exchange J bet... more Linear Heisenberg antiferromagnets (HAFs) are chains of spinS sites with isotropic exchange J between neighbors. Open and periodic boundary conditions return the same ground state energy per site in the thermodynamic limit, but not the same spin SG when S ≥ 1. The ground state of open chains of N spins has SG = 0 or S, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities ρ(r, N) of edge states in HAFs with S = 1, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with ρ(r, N) ∝ (−1) r−1 for r = 1, 2,. .. N. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy Γ(N) that decreases exponentially with N for integer S and faster than 1/N for half integer S. The spin densities and excitation energy are quantitatively modeled for integer S chains longer than 5ξ spins by two parameters, the correlation length ξ and the SDW amplitude, with ξ = 6.048 for S = 1 and 49.0 for S = 2. The BI-SDWs of S = 3/2 chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases |Γ(N)| and weakens the size dependence. The nonlinear sigma model (NLσM) has been applied the HAFs, primarily to S = 1 with even N , to discuss spin densities and exchange between localized states at the ends as Γ(N) ∝ (−1) N exp(−N/ξ). S = 1 chains with odd N are fully consistent with the NLσM; S = 2 chains have two gaps Γ(N) with the same ξ as predicted whose ratio is 3.45 rather than 3; the NLσM is more approximate for S = 3/2 chains with even N and is modified for exchange between ends for odd N .

Physical Review B, 2016

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y-... more An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y-junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 ≈ 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in halffilled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA = NB. The ground state (GS) and spin densities ρr =< S z r > at site r are quite different for junctions with S = 1/2, 1, 3/2 and 2. The GS has finite total spin SG = 2S(S) for even (odd) N and for MG = SG in the SG spin manifold, ρr > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized Sz = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave (SDW) with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Physica B: Condensed Matter, 2010

The bond order wave (BOW) phase of half-filled linear Hubbard-type models is narrow and difficult... more The bond order wave (BOW) phase of half-filled linear Hubbard-type models is narrow and difficult to characterize aside from a few ground state properties. The BOW phase of a frustrated Heisenberg spin chain is wide and tractable. It has broken inversion symmetry C i in a regular array and finite gap E m to the lowest triplet state. The spin-BOW is exact in finite systems at a special point. Its elementary excitations are spin-1/2 solitons that connect BOWs with opposite phase. The same patterns of spin densities and bond orders appear in the BOW phase of Hubbard-type models. Infrared (IR) active lattice phonons or molecular vibrations are derivatives of P, the polarization along the stack. Molecular vibrations that are forbidden in regular arrays become IR active when C i symmetry is broken. 1:1 alkali-TCNQ salts contain half-filled regular TCNQstacks at high temperature, down to 100 K in the Rb-TCNQ(II) polymorph whose magnetic susceptibility and polarized IR spectra indicate a BOW phase. More complete modeling will require explicit electronic coupling to phonons and molecular vibrations.

Physical Review B, 2010

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J1, J2 between first and second nei... more The linear spin-1/2 Heisenberg antiferromagnet with exchanges J1, J2 between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J2/J1 = 0.2411 and is particularly simple at J2/J1 = 1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry and a finite energy gap Em to the lowest triplet state. The interval 0.4 < J2/J1 < 1.0 has large Em and small finite size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large Em are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility χM (T) is exponentially small for T ≪ Em and increases nearly linearly with T to a broad maximum. J1, J2 spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-TCNQ salts.