Finite-temperature Gutzwiller approximation and the phase diagram of a toy-model for V2O3

TL;DR

This paper extends the Gutzwiller approximation to finite temperatures using entropy inequalities, applying it to a two-orbital model of V2O3 and comparing results with dynamical mean field theory.

Contribution

It introduces a finite-temperature variational principle for Gutzwiller and Jastrow trial density matrices and applies it to a model capturing key features of V2O3.

Findings

The phase diagram of the model resembles that of real V2O3.

Finite temperature Gutzwiller approximation provides a rigorous upper bound on free energy.

Results compare well with dynamical mean field theory on a Bethe lattice.

Abstract

We exploit exact inequalities that refer to the entropy of a distribution to derive a simple variational principle at finite temperature for trial density matrices of Gutzwiller and Jastrow type. We use the result to extend at finite temperature the Gutzwiller approximation, which we apply to study a two-orbital model that we believe captures some essential features of V$_2$O$_3$. We indeed find that the phase diagram of the model bears many similarities to that of real vanadium sesquioxide. In addition, we show that in a Bethe lattice, where the finite temperature Gutzwiller approximation provides a rigorous upper bound of the actual free energy, the results compare well with the exact phase diagram obtained by the dynamical mean field theory.