Compressibility and entropy of cold fermions in one dimensional optical lattices

TL;DR

This paper calculates thermodynamic properties of one-dimensional fermions in optical lattices using Bethe-ansatz, providing insights into phase transitions and experimental detection methods.

Contribution

It offers a comprehensive analysis of thermodynamic quantities for 1D fermions at various temperatures and interactions, aiding phase identification in experiments.

Findings

Thermodynamic quantities indicate phase transitions.

Measurement schemes for entropy and compressibility are proposed.

Characteristic features reveal phase coexistence in traps.

Abstract

We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions.We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical potential, we calculate the particle number density, the double occupancy, various compressibilities, and the entropy as a function of temperature and interaction. We find that these thermodynamic quantities show a characteristic behavior so that measurements of these quantities can be used as a detection of temperature, the metal-insulator transition, and metallic and insulating phases in the trap environment. Further, we discuss an experimental scheme to extract these thermodynamic quantities from the column density profiles. The entropy and the compressibility of the entire trapped atomic cloud also reveal characteristic features indicating whether insulating and/or metallic phases coexist in the trap.