T-W relation and free energy of the Heisenberg chain at a finite temperature

Abstract

A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t-W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corresponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

References in corpus (35)

• Review of AdS/CFT Integrability: An Overview
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Separation of Variables. New Trends.
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory
• Density Matrix Renormalization Group Method for 2D Classical Models
• Diffusion and ballistic transport in one-dimensional quantum systems
• The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents
• Density matrix renormalisation group for a quantum spin chain at non-zero temperature
• On the finite temperature Drude weight of the anisotropic Heisenberg chain
• The half-infinite XXZ chain in Onsager's approach
• Thermodynamics of quantum Heisenberg spin chains
• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• Zigzag spin chains with antiferromagnetic-ferromagnetic interactions: Transfer-matrix renormalization group study
• Exact thermodynamics and Luttinger liquid properties of the integrable t-J model
• From Fusion Hierarchy to Excited State TBA
• Analytic Bethe ansatz and functional equations for Lie superalgebra sl(r+1|s+1)
• Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain
• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Accurate computation of low-temperature thermodynamics for quantum spin chains
• Anti-Symmetrically Fused Model and Non-Linear Integral Equations in the Three-State Uimin-Sutherland Model
• Exact Thermodynamics of Disordered Impurities in Quantum Spin Chains
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Exact ground state and elementary excitations of a topological spin chain
• Simplification of thermodynamic Bethe-ansatz equations
• Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
• Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model
• Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field
• Thermodynamics of antiferromagnetic alternating spin chains
• Thermodynamics of a one-dimensional S=1/2 spin-orbital model
• Off-diagonal Bethe Ansatz on the $so(5)$ spin chain
• Off-diagonal Bethe Ansatz for the $D_3^{(1)}$ model

Cited by in corpus (2)

• Off-diagonal approach to the exact solution of quantum integrable systems
• Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector