Thermodynamic Relations in Correlated Systems

TL;DR

This paper derives and confirms thermodynamic relations for metal-insulator transitions in correlated systems, providing constraints on phase boundary shapes and critical properties across various models and dimensions.

Contribution

It generalizes thermodynamic relations for metal-insulator transitions, applicable across dimensions and phases, and confirms their validity in Hubbard and extended models.

Findings

Relations relate thermodynamic quantities to phase boundary slopes.

At continuous Mott transition, diverging charge compressibility implies diverging doublon susceptibility.

First-order phase boundary becomes parallel to temperature axis at zero temperature.

Abstract

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.