# Mott physics beyond Brinkman-Rice scenario

## TL;DR

This paper enhances the Brinkman-Rice approach to the Mott transition by incorporating high-energy virtual processes via a variational Schrieffer-Wolff transformation, achieving results close to dynamical mean-field theory in a Bethe lattice.

## Contribution

It introduces a novel method combining Brinkman-Rice and Schrieffer-Wolff transformation to better capture high-energy processes in Mott transitions.

## Key findings

- The method accurately reproduces the Mott transition in the Bethe lattice.
- Results closely match those from dynamical mean-field theory.
- The approach offers potential for studying more complex models.

## Abstract

The main flaw of the well-known Brinkman-Rice description, obtained through the Gutzwiller approximation, of the paramagnetic Mott transition in the Hubbard model is in neglecting high-energy virtual processes that generate for instance the antiferromagnetic exchange $J\sim t^2/U$. Here we propose a way to capture those processes by combining the Brinkman-Rice approach with a variational Schrieffer-Wolff transformation, and apply this method to study the single-band metal-to-insulator transition in a Bethe lattice with infinite coordination number, where the Gutzwiller approximation becomes exact. We indeed find for the Mott transition a description very close to the real one provided by dynamical mean-field theory; an encouraging result in view of possible applications to more involved models.