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arXiv:cond-mat/9606183 · Physical review. B, Condensed matter

Low-energy properties of antiferromagnetic spin-1/2 Heisenberg ladders with an odd number of legs

Beat Frischmuth, Stephan Haas, Germán Sierra, Thomas Maurice Rice

Published Feb 1, 1997• 29 citations
arXivHTMLPDF

Abstract

An effective low-energy description for multileg spin- Heisenberg ladders with an odd number of legs is proposed. Using a recently developed Monte Carlo loop algorithm and exact-diagonalization techniques, the uniform and staggered magnetic susceptibility and the entropy are calculated for ladders with one, three, and five legs. These systems show a low-temperature scaling behavior similar to spin- 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.

DOI
10.1103/physrevb.55.r3340

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An effective low-energy description for multileg spin- Heisenberg ladders with an odd number of legs is proposed. Using a recently developed Monte Carlo loop algorithm and exact-diagonalization techniques, the uniform and staggered magnetic susceptibility and the entropy are calculated for ladders with one, three, and five legs. These systems show a low-temperature scaling behavior similar to spin- 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.
The temperature dependence of the uniform susceptibility and the ground-state energy of antiferromagnetic Heisenberg ladders with up to six legs has been calculated, using the Monte Carlo loop algorithm. The susceptibilities of even-leg ladders show spin gaps while those of odd-leg ladders remain finite in the zero-temperature limit. For small ratios of intra- to interleg couplings, odd-leg ladders can be mapped at low temperatures to single chains. For equal couplings, the logarithmic corrections at low temperatures increase markedly with the number of legs.
Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.
Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( r=0r=0r=0 r = 0 ) case up to the diluted ( r→1r \rightarrow 1r→1 r → 1 ) limit, and for selected choices of number of legs LyL_yLy​ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing LyL_yLy​ L y . Graphical Abstract
A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.