Nonlinear Integral Equations for Thermodynamics of the $U_{q}(\widehat{sl(r+1)})$ Perk–Schultz ModelNonlinear Integral Equations for Thermodynamics of the $U_{q}(\widehat{sl(r+1)})$ Perk–Schultz Model

Zengo Tsuboi, Minoru Takahashi

We propose a system of nonlinear integral equations (NLIE) which describes the thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz model. These NLIE correspond to a trigonometric analogue of our previous result (cond-mat/0212280), and contain only r unknown functions. In particular, they reduce to Takahashi's NLIE for the XXZ spin chain (cond-mat/0010486) if r=1. We also calculate the high temperature expansion of the free energy. In particular for r=1 case, we have succeeded to derive the coefficients of order O((\frac{J}{T})^{99}).We propose a system of nonlinear integral equations (NLIE) which describes the thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz model. These NLIE correspond to a trigonometric analogue of our previous result (cond-mat/0212280), and contain only r unknown functions. In particular, they reduce to Takahashi's NLIE for the XXZ spin chain (cond-mat/0010486) if r=1. We also calculate the high temperature expansion of the free energy. In particular for r=1 case, we have succeeded to derive the coefficients of order O((\frac{J}{T})^{99}).

arXiv:cond-mat/0412698Journal of the Physical Society of JapanMar 1, 20059 citations

New method of deriving high temperature expansions for the Heisenberg model

Cyril Domb, David W. Wood

Physics LettersJan 1, 196421 citations

Thermodynamics of the quantum Perk - Schultz model

Andreas Klümper, T Wehner, J. Zittartz

The quantum mechanical analogue of the classical Perk - Schultz model is considered which comprises the Uimin - Sutherland model and the integrable t - J chain. The quantum transfer matrix of these systems is established and the eigenvalue equations are obtained by an algebraic Bethe ansatz. Only the largest eigenvalue is needed for the calculation of the free energy of the quantum chain at finite temperature. The Bethe ansatz equations for the leading eigenvalue are transformed into a set of integral equations for some appropriately defined auxiliary functions. Furthermore, the eigenvalue of the quantum transfer matrix is expressed in terms of these functions. The integral formulation allows for taking the limit of infinite Trotter - Suzuki number analytically. The low-temperature limit of the free energy is obtained analytically and for intermediate temperatures numerical results are presented.The quantum mechanical analogue of the classical Perk - Schultz model is considered which comprises the Uimin - Sutherland model and the integrable t - J chain. The quantum transfer matrix of these systems is established and the eigenvalue equations are obtained by an algebraic Bethe ansatz. Only the largest eigenvalue is needed for the calculation of the free energy of the quantum chain at finite temperature. The Bethe ansatz equations for the leading eigenvalue are transformed into a set of integral equations for some appropriately defined auxiliary functions. Furthermore, the eigenvalue of the quantum transfer matrix is expressed in terms of these functions. The integral formulation allows for taking the limit of infinite Trotter - Suzuki number analytically. The low-temperature limit of the free energy is obtained analytically and for intermediate temperatures numerical results are presented.

Journal of Physics A Mathematical and GeneralMar 21, 199719 citations

14aPS-11 U_q(sl(r+1)) Perk-Schultz 模型に対する r 個しか未知函数を含まない積分方程式(ポスターセッション, 領域 11)

禅吾坪井, 實高橋

日本物理学会講演概要集Aug 25, 20040 citations

High-temperature series expansion for spin-1/2 Heisenberg models

Andreas Hehn, Natalija van Well, Matthias Troyer

arXiv:1609.01878Computer Physics CommunicationsOct 9, 201617 citations

Nonlinear Integral Equations for Thermodynamics of the

U_{q}(\widehat{sl(r+1)})

Perk–Schultz Model