# Excitations and correlations in the driven-dissipative Bose-Hubbard model

## TL;DR

This paper investigates the driven-dissipative Bose-Hubbard model using a field-theoretic approach, revealing complex phase behavior, excitations, and correlations influenced by driving and losses.

## Contribution

It introduces a detailed analysis of the phase diagram and excitation regimes of the driven-dissipative Bose-Hubbard model using the Schwinger-Keldysh formalism.

## Key findings

- Identification of bistability and phase regimes
- Discovery of dynamically unstable, gapped, and gapless phases
- Correlation length increases in the gapless regime

## Abstract

Using a field-theoretic approach within the Schwinger-Keldysh formalism, we study a Bose-Hubbard model in the presence of a driving field and dissipation due to one-body losses. We recover the bistability diagram from the Gross-Pitaevski equation and analyze the different phases with respect to their elementary excitations and correlations. We find the low-density solution to be subdivided into a dynamically instable, a gapped, and a gapless regime. The correlations decay exponentially, but a substantial increase of correlation length marks the regime of gapless excitations.