Composite fermion-boson mapping for fermionic lattice models

TL;DR

This paper introduces an exact mapping of fermionic operators to composite fermion-boson operators, enabling an efficient mean-field approach to study the Mott insulator phase in Hubbard models.

Contribution

It proposes a novel exact isomorphism mapping fermions to composite particles and develops a mean-field method to analyze strongly correlated lattice systems.

Findings

Accurately describes the Mott insulating phase of Hubbard models.

Provides a computationally efficient mean-field approach.

Validates the method on 1D and 2D Hubbard models.

Abstract

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the one- and two-dimensional Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.