Dynamic Phase Diagram for the Quantum Phase Model

TL;DR

This paper investigates the stability of superfluid currents in lattice bosons using the quantum phase model, deriving analytical critical lines for instabilities and validating them against numerical results.

Contribution

It introduces analytical expressions for critical stability lines in the quantum phase model, enhancing understanding of superfluid current stability in lattice bosons.

Findings

Analytical critical lines match numerical results.

Superfluid current stability depends on modulational and energetic instabilities.

Quantum phase model effectively approximates Bose-Hubbard behavior in large interactions.

Abstract

We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approximation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and energetic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model.