Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

TL;DR

This paper introduces a contour-time formalism for analyzing space-time correlations in the Bose-Hubbard model, applicable to both equilibrium and non-equilibrium states, and compares its accuracy with existing methods.

Contribution

It develops a two-particle irreducible effective action within the contour-time framework for the Bose-Hubbard model, enabling study of correlations in and out of equilibrium.

Findings

Formalism accurately reproduces known results in equilibrium.

Provides a new tool for studying out-of-equilibrium dynamics.

Shows good agreement with existing strong coupling methods.

Abstract

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations.