Free energy and correlation lengths of quantum chains related to restricted solid‐on‐solid lattice models

Abstract

An approach is presented for calculating the free energy as well as the correlation lengths of integrable quantum chains at arbitrary finite temperatures. The method is applied to critical Hamiltonians related to restricted solid-on-olid models comprising the hierarchy by Andrews, Baxter and Forrester, and generalizations hereof by the fusion procedure. The derived non-linear integral equations can be studied analytically in the low-temperature and high-temperature limits. The central charges and all primary conformal weights are obtained for the generalized minimal unitary series of conformal field theory and the Z , parafermion theories. Thus an extension of the thermodynamic Bethe Ansatz is realized which recently has been speculated on in the literature.

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

“…The free energy per lattice site of the system is given by the following set of non-linear integral equations [18] for auxiliary functions a, and…”

“…In Fig. 1 the specific heat c(T ), susceptibility χ(T ) and correlation length ξ(T ) (computed on the basis of [18]) at zero field are presented. Note the divergence of ξ(T ) at low temperatures.…”

“…In Section 2 of this paper an approach to the thermodynamics on the basis of the physical excitations (spinons) is applied to the study of several thermodynamical properties [18] (see also the related approach by [19,20,21,22,23,24,25,26]). The main results concern the numerical and analytical calculation of the universal leading and next-leading corrections in the susceptibility.…”

Nonlinear integral equations for thermodynamics of thesl(r 1) Uimin Sutherland model

“…In the context of the QTM method, for models related to algebras of rank one or two, nonlinear integral equations (NLIE) with finite numbers of unknown functions were derived by Klümper and his collaborators [9,14,15,16,17,18]. Although their NLIE give the same free energy as TBA equations, the derivations need trial and error for each model, which prevents their extension to higher rank case.…”

Transfer matrix eigenvalues of the anisotropic multiparametricUmodel

“…The quantum transfer matrix approach, which has primarily been developed by Klümper and collaborators [38,39,40], has proved to be a powerful method to determine thermodynamic properties of an integrable model at finite temperature. In the final section of this work we will present the eigenvalues of the quantum transfer matrix for the anisotropic multiparametric U model.…”