Density-functional theory approach to the thermodynamics of the harmonically confined one-dimensional Hubbard model

TL;DR

This paper develops a density-functional theory method, based on local-density approximation and thermodynamic Bethe ansatz, to study the thermodynamics of inhomogeneous one-dimensional Hubbard models with confinement, revealing unusual behaviors during isentropic expansion.

Contribution

It introduces a DFT approach using TBALDA for inhomogeneous 1D Hubbard models, combining exact homogeneous results with classical thermodynamics for large systems.

Findings

Good agreement between TBALDA and exact diagonalization for small chains

Identification of unusual behavior during isentropic expansion

Development of a classical thermodynamic framework for large systems

Abstract

The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic Hubbard model with parabolic confinement is studied by a density-functional theory approach, based on Mermin's generalization to finite temperatures. A local-density approximation (LDA), based on exact results for the homogeneous model, is used to approximate the correlation part in the Helmholtz free-energy, comprising the thermodynamic Bethe ansatz LDA (TBALDA). The general presentation of the method is given and some properties of the homogeneous model that are relevant to the DFT approach are analyzed. Extensive comparison between TBALDA and numerical exact diagonalization results for thermodynamic properties of small inhomogeneous chains is discussed. In the remaining, a classical thermodynamic treatment of the confined system is developed with the focus on global properties of large systems. A unusual behavior under isentropic expansion is found and discussed.