Thermodynamics and Crossover Phenomena in the Correlation Lengths of the One-Dimensional t-J Model

TL;DR

This paper studies the thermodynamics and correlation phenomena in the one-dimensional t-J model, confirming phase diagrams, analyzing crossover behaviors, and comparing numerical results with theoretical predictions.

Contribution

It provides detailed TMRG calculations of thermodynamic quantities and correlation lengths, validating phase diagrams and theoretical models for the 1D t-J system.

Findings

Confirmation of phase diagram with TLL and phase-separated states

Observation of spin-gap phase near phase separation

Agreement with Bethe ansatz and CFT predictions

Abstract

We investigate the thermodynamics of the one-dimensional t-J model using transfer matrix renormalization group (TMRG) algorithms and present results for quantities like particle number, specific heat, spin susceptibility and compressibility. Based on these results we confirm a phase diagram consisting of a Tomonaga-Luttinger liquid (TLL) phase for small J/t and a phase separated state for J/t large. Close to phase separation we find a spin-gap (Luther-Emery) phase at low densities consistent with predictions by other studies. At the supersymmetric point we compare our results with exact results from the Bethe ansatz and find excellent agreement. In particular we focus on the calculation of correlation lengths and static correlation functions and study the crossover from the non-universal high T lattice into the quantum critical regime. At the supersymmetric point we compare in detail with predictions by conformal field theory (CFT) and TLL theory and show the importance of logarithmic corrections.