Dynamic structure factor of a driven-dissipative Bose-Hubbard model

TL;DR

This paper calculates the dynamic structure factor of a driven-dissipative Bose-Hubbard model to identify signatures of dissipative phase transitions, using a mean-field approach combined with Lindbladian perturbation to analyze density fluctuations.

Contribution

It introduces a combined mean-field and Lindbladian perturbation method to study density fluctuations near dissipative phase transitions in open quantum lattice systems.

Findings

DSF signature distinctly changes near the DPT

Mean-field results serve as benchmarks for LPM

Method offers computationally feasible analysis of open quantum systems

Abstract

Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase transitions of ultracold atoms are addressed by harnessing density fluctuations. Here, we calculate the DSF of a nonequilibrium spinless Bose-Hubbard model (BHM) from the perspective of dissipative phase transition (DPT) in a steady state. Our methodology uses a homogeneous mean-field approximation to make the single-site hierarchy simpler and applies the Lindbladian perturbation method (LPM) to go beyond the single site, limited by the ratio of the inter-site hopping term to the Liouvillian gap as a small parameter. Our results show that the DSF near a DPT point is characteristically different from that away from the transition point, providing a clear density spectral signature of the DPT. In addition to comparing the two numerical frameworks, the mean-field results serve as a benchmark for proof-of-principle robustness of LPM. Despite the numerical difficulty, our methodology provides a computationally accessible route for studying density fluctuations in an open lattice quantum system without requiring large-scale computation.