Quantum phase diagram of a frustrated spin- 12 system on a trellis ladder (original) (raw)
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Phase diagram of the frustrated spin ladder
Physical Review B, 2010
We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J ⊥ and diagonal coupling J×. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J ⊥ = 2J×. Following this insight we then suggest that changing these competing inter-chain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density matrix renormalization group and exact diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic J ⊥ and J× is determined.
Phase diagrams of spin ladders with ferromagnetic legs
Physical Review B, 2003
The low-temperature properties of the spin S = 1/2 ladder with anisotropic ferromagnetic legs are studied using the continuum limit bosonization approach. The weak-coupling ground state phase diagram of the model is obtained for a wide range of coupling constants and several unconventional gapless "spin-liquid" phases are shown to exist for ferromagnetic coupling. The behavior of the ladder system in the vicinity of the ferromagnetic instability point is discussed in detail.
Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder
Physical Review B
The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and seven-membered 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 (J 2 = 1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J 1) along the rungs. As a function of J 1 , the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various 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 J 1 ; the ferrimagnetic phase with gs spin S G = n for 1.44 < J 1 < 4.74 and with S G = 2n for J 1 > 5.63, where n is the number of unit cells; and a reentrant nonmagnetic phase at 4.74 < J 1 < 5.44. The system also shows the presence of spin current at specific J 1 values due to simultaneous breaking of both reflection and spin parity symmetries.
Physical Review B, 2012
We study the ground-state (GS) properties of the frustrated spin-1 2 J 1-J 2-J 3 Heisenberg model on the two-dimensional honeycomb lattice with ferromagnetic nearest-neighbor (J 1 = −1) exchange and frustrating antiferromagnetic next-nearest-neighbor (J 2 > 0) and next-next-nearest-neighbor (J 3 > 0) exchanges, for the case J 3 = J 2. We use the coupled-cluster method implemented to high orders of approximation, complemented by the Lanczos exact diagonalization of a large finite lattice with 32 sites, in order to calculate the GS energy, magnetic order parameter, and spin-spin correlation functions. In one scenario we find a quantum phase transition point between regions characterized by ferromagnetic order and a form of antiferromagnetic ("striped") collinear order at J c 2 ≈ 0.1095 ± 0.0005, which is below the corresponding hypothetical transition point at J cl 2 = 1 7 (≈0.143) for the classical version of the model, in which we momentarily ignore the intervening noncollinear spiral phase in the region 1 10 < J 2 < 1 5. Hence we see that quantum fluctuations appear to stabilize somewhat the collinear antiferromagnetic order in preference to the ferromagnetic order in this model. We compare results for the present ferromagnetic case (with J 1 = −1) to previous results for the corresponding antiferromagnetic case (with J 1 = +1). The magnetic order parameter is found to behave similarly for the ferromagnetic and the antiferromagnetic models for large values of the frustration parameter J 2. However, there are considerable differences in the behavior of the order parameters for the two models for J 2 /|J 1 | 0.6. For example, the quasiclassical collinear magnetic long-range order for the antiferromagnetic model (with J 1 = +1) breaks down at J c 2 2 ≈ 0.60, whereas the "equivalent" point for the ferromagnetic model (with J 1 = −1) occurs at J c 2 ≈ 0.11. Unlike in the antiferromagnetic model (with J 1 = +1), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical antiferromagnetic phases (with Néel and striped order) for J c 1 2 < J 2 < J c 2 2 , with J c 1 2 ≈ 0.47, we find no clear indications at all in the ferromagnetic model for an intermediate magnetically disordered phase between the corresponding phases exhibiting ferromagnetic and striped order. Instead the evidence for the ferromagnetic model (with J 1 = −1) points to one of two scenarios: either there is a direct first-order transition between the two magnetically ordered phases, as mentioned above; or there exists an intervening phase between them in the very narrow range 0.10 J 2 0.12, which is probably a remnant of the spiral phase that exists in the classical counterpart of the model over the larger range 1 10 < J 2 < 1 5 .
Magnetic properties of a quantum spin ladder in proximity to the isotropic limit
Physical Review B, 2021
We report on the synthesis, crystal structure, magnetic, thermodynamic, and electron-spinresonance (ESR) properties of the coordination complex [Cu2(pz)3(4-HOpy)4](ClO4)4 [pz = pyrazine; 4-HOpy = 4-hydroxypyridine]. This material is identified as a spin-1/2 Heisenberg ladder system with exchange-coupling parameters Jrung/kB = 12.1(1) K and J leg /kB = 10.5(3) K [Jrung/J leg = 1.15(4)]. For single crystals our measurements revealed two critical fields, µ0Hc1 = 4.63(5) T and µ0Hc2 = 22.78(5) T (for H ∥ a *), separating the gapped spin-liquid, gapless Tomonaga-Luttinger-liquid, and fully spin-polarized phase. No signature of a field-induced transition into a magnetically ordered phase was found at temperatures down to 0.5 K. The material bridges an important gap by providing an excellent physical realization of an almost isotropic spin-1/2 strong-rung Heisenberg ladder system with modest exchange-coupling energy and critical-field scales.
The European Physical Journal B, 2019
We study the ground-state magnetic phase diagram of a spin S = 1/2 antiferromagnetic two-leg ladder in the presence of period two lattice units modulated, Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto the effective spin σ = 1/2 XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M = 0 and to its saturation value per rung M = Msat = 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M = 0.5Msat. The width of the magnetization plateau at M = 0.5Msat, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (D0D1/J 2) α where D0, D1 are uniform and staggered components of the DM term, J is the intraleg exchange and α ≤ 3/4 and weakly depends on the DM couplings.
Physical Review B, 2007
We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using two-dimensional density-matrix renormalization group method. Calculating the gound-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120-degree antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model and find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs but those in the magnetically ordered phases are non-degenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.
Quantum phases of frustrated two-leg spin- 12 ladders with skewed rungs
Physical Review B, 2017
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.