Self-consistent Keldysh approach to quenches in weakly interacting Bose-Hubbard model

TL;DR

This paper introduces a self-consistent Keldysh Green's function method to analyze non-equilibrium dynamics in weakly interacting Bose-Hubbard models after a quench, capturing the transition from ballistic to diffusive behavior.

Contribution

It develops a numerically implementable self-consistent Green's function approach based on Hedin's equations for studying quenches in Bose-Hubbard models.

Findings

The method recovers the crossover from ballistic to diffusive regimes.

High-temperature initial states can restore ballistic dynamics.

The approach is effective for both 1D and 2D systems.

Abstract

We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemented numerically by a parallelized code. We exploit this approach to study the correlation propagation after a quench in the interaction parameter, for one (1D) and two (2D) dimensions. In particular, we show how our approach is able to recover the crossover from ballistic to diffusive regime by increasing the boson-boson interaction. Finally we also discuss the role of a thermal initial state on the dynamics both for 1D and 2D Bose Hubbard models, finding that surprisingly at high temperature a ballistic evolution is restored.