Effective lattice actions for correlated electrons

TL;DR

This paper introduces an exact operator representation and a path-integral approach for the $t$-$J$ and Hubbard models, linking them to other models and exploring semiclassical limits.

Contribution

It provides a novel exact representation of electron operators and extends the functional approach to the Hubbard model, establishing new theoretical connections.

Findings

Exact, unconstrained electron operator representation.

Path-integral formulation for the $t$-$J$ model with a semiclassical parameter.

Mean-field theory equivalence to the Falikov--Kimball model.

Abstract

We present an exact, unconstrained representation of the electron operators in terms of operators of opposite statistics. We propose a path--integral representation for the $t$-$J$ model and introduce a parameter controlling the semiclassical behaviour. We extend the functional approach to the Hubbard model and show that the mean--field theory is equivalent to considering, at Hamiltonian level, the Falikov--Kimball model. Connections with a bond-charge model are also discussed.