Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model (original) (raw)
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Incommensurate nodes in the energy spectrum of coupled antiferromagnetic Heisenberg ladders
Physical Review B, 1997
Heisenberg ladders are investigated using the bond-mean-field theory [M.Azzouz, Phys.Rev.B 48, 6136 (1993)]. The zero inter-ladder coupling energy gap, the uniform spin susceptibility and the nuclear magnetic resonance spin-relaxation rate are calculated as a function of temperature and magnetic field. For weakly coupled ladders, the energy spectrum vanishes at incommensurate wavevectors giving rise to nodes. As a consequence, the spin susceptibility becomes linear at low temperature. Our results for the single ladder successfully compare to experiments on SrCu2O3 and (VO)2P2O7 materials and new predictions concerning the coupling to the magnetic field are made. PACS number(s): 75.30.Ee, 75.30.Kz, 75.10.Jm
Physical Review B, 2007
We obtain the phase diagram in the parameter space (J′/J,gamma)(J'/J, \gamma)(J′/J,gamma) and an accurate estimate of the critical line separating the different phases. We show several measuments of the magnetization, dimerization, nearest neighbours correlation, and density of energy in the different zones of the phase diagram, as well as a measurement of the string order parameter proposed as the non vanishing phase order parameter characterizing Haldane phases. All these results will be compared in the limit J′/Jgg1J'/J\gg 1J′/Jgg1 with the behaviour of the textbfS=1\textbf{S}=1textbfS=1 Bond Alternated Heisenberg Chain (BAHC). The analysis of our data supports the existence of a dimer phase separated by a critical line from a Haldane one, which has exactly the same nature as the Haldane phase in the textbfS=1\textbf{S}=1textbfS=1 BAHC.
Magnetic order in ferromagnetically coupled spin ladders
Physical Review B, 2000
A model of coupled antiferromagnetic spin-1/2 Heisenberg ladders is studied with numerical techniques. In the case of ferromagnetic interladder coupling we find that the dynamic and static structure factor has a peak at (pi,pi/2)(\pi,\pi/2)(pi,pi/2) where the first (second) direction is along (transversal) to the ladders. Besides, we suggest that the intensity of this peak and the spin-spin correlation at the maximum distance along the ladder direction remain finite in the bulk limit for strong enough interladder coupling. We discuss the relevance of these results for magnetic compounds containing ladders coupled in a trellis lattice and for the stripe scenario in high-T$_c$ superconducting cuprates.
Scaling theory of antiferromagnetic Heisenberg ladder models
Journal of Physics A: Mathematical and General, 1995
The S = 1/2 antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as ∆E ∼ J ⊥ , where J ⊥ is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge c = 1 extends over the whole region of J ⊥ > 0.
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.
The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain
European Physical Journal B, 2010
By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of 64, 100, 200, 300 sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.
Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg model on a ladder
Physical Review B, 1994
The ground state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean field theory and the density matrix renormalization group. Spin wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, J ⊥ , in the ladder. It is found that the gap is linear in J ⊥ for J ⊥ ≫ 1 and goes to zero for J ⊥ → 0. The mean field theory agrees well with the numerical results.
Ordering in Linear Antiferromagnetic Chains with Anisotropic Coupling
Physical Review, 1966
Some reasonable conjectures are made concerning the Gnite-temperature pair correlations of spins with anisotropic antiferromagnetic coupling. These conjectures provide a general description of the ordering. Using them together with the Gnite value of the zero-temperature susceptibility, one obtains Sg &S3 «.. . 0. .. «S4 &Sl, where S =1-(-1)"co"+2Z(og, co~is the zero-temperature pair correlation, and s&" is the infinite-/ limit of~a~i). Bonner and Fisher's finitechain extrapolations for &oi are in agreement with this result. Using their values of cut (f = 1&2P&4&~) and the inequality, bounds are computed for u5. The further conjecture that the rate of decrease in the absolute value of the correlation with distance is monotonic leads to a contradiction near the Heisenberg limit. The role of co" in the inequality and its derivation is particularly interesting since the limit l~~followed by T-+ 0 of the pair correlation of spins separated by t-1 spins is probably zero and not co. When the correlations approximate their zero-temperature value out to a distance g such that (cps) =id"and decrease slowly thereafter with increasing separation, then Tx is approximately zero.
Low-energy properties of antiferromagnetic spin-1/2 Heisenberg ladders with an odd number of legs
Physical Review B, 1997
An effective low-energy description for multi-leg spin-1/2 Heisenberg ladders with an odd number of legs is proposed. Using a newly developed Monte Carlo loop algorithm and exact diagonalization techniques, the uniform and staggered magnetic susceptibility and the entropy are calculated for ladders with 1, 3, and 5 legs. These systems show a low-temperature scaling behavior similar to spin-1/2 chains with longer ranged unfrustrated exchange interactions. The spinon velocity does not change as the number of legs increases, but the energy scale parameter decreases markedly.
Physical Review B, 2014
We present specific-heat and neutron-scattering results for the S =1/2 quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)CuBr4. The material orders magnetically at T N =1.99(2) K, and magnetic excitations are accompanied by an energy gap of 0.30(2) meV due to spin anisotropy. The system is best described as coupled two-leg spin-1/2 ladders with the leg exchange J leg =0.60(2) meV, rung exchange Jrung=0.64(9) meV, interladder exchange Jint=0.19(2) meV, and an interaction-anisotropy parameter λ=0.93(2), according to inelastic neutron-scattering measurements. In contrast to most spin ladders reported to date, the material is a rare example in which the interladder coupling is very near the critical value required to drive the system to a Néel-ordered phase without an assistance of a magnetic field.