From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
نویسنده
چکیده
We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (BazhanovReshetikhin formula), which gives the solution of the T -system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility. Short title: Nonlinear integral equation MSC: 82B23; 45G15; 82B20; 17B80 PACS2001: 02.30.Rz; 02.30.Ik; 05.50.+q; 05.70.-a
منابع مشابه
Nonlinear Integral Equations and High Temperature Expansion for the U Q ( Sl(r + 1|s + 1)) Perk-schultz Model
We propose a system of nonlinear integral equations (NLIE) which gives the free energy of the Uq(ŝl(r+1|s+1)) Perk-Schultz model. In contrast with traditional thermodynamic Bethe ansatz equations, our NLIE contain only r+s+1 unknown functions. In deriving the NLIE, the quantum (supersymmetric) Jacobi-Trudi and Giambelli formula and a duality for an auxiliary function play important roles. By us...
متن کاملThermal negativity in a two qubit XXX and XX spin chain model in an external magnetic field
In this paper we studied the thermal negativity in a two-qubit XX spin ½ chain model and XXX spin1/2 chain model(isotropic Heisenberg model)spin-1/2 chain subjected to an external magnetic field inz direction. We calculate analytical relation for the thermal negativity for two qubit XX and XXX spinchain models in the external magnetic field. Effects of the magnetic field and temperature on then...
متن کاملNonlinear Integral Equations for Thermodynamics of the Sl(r + 1) Uimin-sutherland Model
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r + 1) Uimin-Sutherland model from the T -system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number o...
متن کاملA wavelet method for stochastic Volterra integral equations and its application to general stock model
In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...
متن کاملStable Equivalences of Giambelli Type Matrices of Schur Functions
Abstract. By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to each other over symmetric functions. As a consequence, the Jacobi-Trudi matrix and the dual Jacobi-Trudi matrix are stably equivalent over symmetric functions. This gives an affirmative answer to an open pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003