Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

TL;DR

This paper investigates the thermodynamics of the one-dimensional half-filled Hubbard model in a high-temperature spin-disordered regime, revealing insights into charge excitations, entropy contributions, and a finite-interaction metal-insulator transition.

Contribution

It provides a detailed analysis of the thermodynamic Bethe Ansatz equations in the spin-disordered regime, highlighting temperature independence of energy and dispersion, and connects these findings to the Mott-Hubbard transition.

Findings

Internal energy and dispersion are temperature-independent in the regime.

Charge excitations are gapped with effective dispersion.

A finite-interaction metal-insulator transition occurs with a linear gap opening.

Abstract

We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal-insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott-Hubbard transition in the limit of infinite dimensions.