Exact thermodynamics and Luttinger liquid properties of the integrable t-J model

TL;DR

This paper uses an exact Trotter-Suzuki mapping and quantum transfer matrix approach to analyze the finite-temperature thermodynamics and Luttinger liquid properties of the integrable one-dimensional supersymmetric t-J model, confirming theoretical predictions.

Contribution

It provides the first complete finite-temperature analysis of a strongly correlated lattice electron system using exact methods, including integral equations and conformal field theory validation.

Findings

Exact thermodynamic quantities calculated for the t-J model.

Confirmation of Luttinger liquid and conformal field theory predictions at low temperatures.

Derivation of simplified integral equations for the largest eigenvalue of the quantum transfer matrix.

Abstract

A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric $t-J$ model. This approach allows for the exact calculation of various thermodynamical properties by means of the quantum transfer matrix (QTM). The free energy and other interesting quantities are obtained such as the specific heat and compressibility. For the largest eigenvalue of the QTM leading to the free energy a set of just two non-linear integral equations is presented. These equations are studied analytically and numerically for different particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations. Special emphasis is placed on the study of the low-temperature behavior confirming scaling predictions by conformal field theory and Luttinger liquid theory. To our knowledge this is the first complete investigation of a strongly correlated electron system on a lattice at finite temperature.