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Physical review. B, Condensed matter

Thermodynamics of the exactly solvable two-chain and multichain quantum spin models

Andrei A. Zvyagin

Published May 1, 1995• 33 citations
Publisher

Abstract

The equations of the thermodynamic Bethe ansatz for two-chain and multichain quantum spin 1/2 systems are constructed. It is shown that the system is in the antichiral state for any temperature range and for any value of the external magnetic field (except for the ferromagnetic ground-state case). The elementary spin excitations carry nonzero chirality and are gapless. Those excitations are confined into pairs (singlets and triplets), with opposite sign of chiralities, so the state of the system remains antichiral at any temperature. The reason for such chiral behavior is the existence of the topological term of the Wess-Zumino nature in the Hamiltonian. We conjecture that the quantum spin (1/2) multichain system with the Hamiltonian without the topological terms has excitations with gaps.

DOI
10.1103/physrevb.51.12579

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The equations of the thermodynamic Bethe ansatz for two-chain and multichain quantum spin 1/2 systems are constructed. It is shown that the system is in the antichiral state for any temperature range and for any value of the external magnetic field (except for the ferromagnetic ground-state case). The elementary spin excitations carry nonzero chirality and are gapless. Those excitations are confined into pairs (singlets and triplets), with opposite sign of chiralities, so the state of the system remains antichiral at any temperature. The reason for such chiral behavior is the existence of the topological term of the Wess-Zumino nature in the Hamiltonian. We conjecture that the quantum spin (1/2) multichain system with the Hamiltonian without the topological terms has excitations with gaps.
We have constructed a Bethe ansatz solution for the multichain quantum supersymmetric frustrated t-J model. The system is in the antichiral state for both spin and charge degrees of freedom. Elementary spin and charge excitations carry nonzero chiralities (topological charges) but they are confined into pairs with opposite signs of their chiralities, so the state of the system remains antichiral. Topological terms of Wess-Zumino nature in the Hamiltonian cause such chiral behavior. We conjecture that a multichain supersymmetric frustrated t-J model without topological terms in the Hamiltonian has charge and spin excitations with gaps.
We consider a two-parameter (c\ifmmode\bar\else\textasciimacron\fi{},c\ifmmode \tilde{}\else \~{}\fi{}) family of quantum integrable isotropic Hamiltonians for a chain of alternating spins of spin s=1/2 and s=1. We determine the thermodynamics for low-temperature T and small external magnetic field H, with T\ensuremath{\ll}H. In the antiferromagnetic (c\ifmmode\bar\else\textasciimacron\fi{}>0,c\ifmmode \tilde{}\else \~{}\fi{}>0) case, the model has two gapless excitations. In particular, for c\ifmmode\bar\else\textasciimacron\fi{}=c\ifmmode \tilde{}\else \~{}\fi{}, the model is conformally invariant and has central charge cvir{\mathit{c}}_{\mathrm{vir}}cvir​=2. When one of these parameters is zero, the Bethe ansatz equations admit an infinite number of solutions with lowest energy.
Phase transitions in the quantum frustrated antiferromagnetic two-chain system with additional three-spin interactions of special form are studied. With the help of an exact Bethe ansatz solution it is shown that such a zigzag-like system has two critical-magnetic-field values in the ground state: One of these is the usual phase transition into a ferromagnetic state, while the second one is connected with magnetic structure doubling. Two phase transitions are revealed in the ``factorization'' of the dispersion law of an elementary excitation. The absence of a gap behavior in recent experiments is explained. Two types of chiral spin ordering for frustrated low-dimensional magnets are proposed.
The behavior in an external magnetic field is studied exactly for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate–incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exactly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in the limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrable theories are calculated.
The ground state and thermodynamic properties of spin-1 and spin- chains are investigated via exactly solved su (3) and su (4) models with physically motivated chemical potential terms. The analysis involves the thermodynamic Bethe ansatz and the high temperature expansion (HTE) methods. For the spin-1 chain with large single-ion anisotropy, a gapped phase occurs which is significantly different from the valence-bond-solid Haldane phase. The theoretical curves for the magnetization, susceptibility and specific heat are favourably compared with experimental data for a number of spin-1 chain compounds. For the spin- chain a degenerate gapped phase exists starting at zero external magnetic field. A middle magnetization plateau can be triggered by the single-ion anisotropy term. Overall, our results lend further weight to the applicability of integrable models to the physics of low-dimensional quantum spin systems. They also highlight the utility of the exact HTE method.