Exact path-integral evaluation of locally interacting systems: The subtlety of operator ordering

TL;DR

This paper clarifies how operator ordering affects path-integral calculations in locally interacting systems, resolving previous inconsistencies and offering a new perspective on strongly correlated materials.

Contribution

It reveals the impact of operator ordering on the Hubbard-Stratonovich transformation and demonstrates a novel approach to describe strong interactions via free-particle theory with random potentials.

Findings

Operator ordering subtlety modifies the Hubbard-Stratonovich transformation.

Many-body effects in strong interactions can be captured by free-particle theory with random fields.

The approach broadens the understanding of strongly correlated systems.

Abstract

We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the local interaction term modifies the Hubbard-Stratonovich transformation in the continuous time formulation, and it helps reproduce known results by the operator method. We also demonstrate that many-body effects in the strong interaction limit can be well characterized by the free-particle theory that is subject to annealed random potentials and dynamical gauge (or phase) fields. The present treatment expands the conventional paradigm of the one-particle description, and it provides a simple, viable picture for strongly correlated materials of either bosonic or fermionic systems.