# Coherent state path integral approach to correlated electron systems with deformed Hubbard operators: from Fermi liquid to Mott insulator

## TL;DR

This paper develops a coherent state path integral method for correlated electron systems with deformed Hubbard operators, revealing a continuous transition from Fermi liquid to Mott insulator behavior influenced by a tunable interaction parameter.

## Contribution

It introduces a novel path integral approach applicable to deformed Hubbard operators across all interaction strengths, bridging free and strongly correlated electron regimes.

## Key findings

- System exhibits correlated Fermi liquid behavior with enhanced Wilson ratio for all interaction parameters.
- A finite Mott gap appears with Coulomb interaction, with spectral weight heavily influenced by the deformation parameter.
- The approach is valid in arbitrary spatial dimensions and uncovers complex interplay between hopping and Coulomb repulsion.

## Abstract

In strongly correlated electron systems the constraint which prohibits the double electron occupation at local sites can be realized by either the infinite Coulomb interaction or the correlated hopping interaction described by the Hubbard operators, but they both render the conventional field theory inapplicable. Relaxing such the constraint leads to a class of correlated hopping models based on the deformed Hubbard operators which smoothly interpolate the locally free and strong coupling limits by a tunable interaction parameter $0\leq \lambda\leq 1$. Here we propose a coherent state path integral approach appropriate to the deformed Hubbard operators for {\it arbitrary} $\lambda$. It is shown that this model system exhibits the correlated Fermi liquid behavior characterized by the enhanced Wilson ratio for all $\lambda$. It is further found that in the presence of on-site Coulomb interaction a finite Mott gap appears between the upper and lower Hubbard bands, with the upper band spectral weight being heavily reduced by $\lambda$. Our approach stands in general spatial dimensions and reveals an unexpected interplay between the correlated hopping and the Coulomb repulsion.