# Light-cone and diffusive propagation of correlations in a many-body dissipative system

## TL;DR

This paper studies how correlations spread in a strongly interacting quantum system with dissipation, revealing that dissipation can accelerate correlation propagation but also cause decoherence, with different behaviors for single-particle and density correlations.

## Contribution

It demonstrates the effects of dissipation on correlation dynamics in a Bose-Hubbard system, combining numerical simulations with a fermionic quasi-particle approach for detailed insights.

## Key findings

- Dissipation speeds up single-particle correlation propagation.
- Density correlations transition from ballistic to diffusive behavior.
- Numerical and analytical methods agree on the dynamics.

## Abstract

We analyze the propagation of correlations after a sudden interaction change in a strongly interacting quantum system in contact with an environment. In particular, we consider an interaction quench in the Bose-Hubbard model, deep within the Mott-insulating phase, under the effect of dephasing. We observe that dissipation effectively speeds up the propagation of single-particle correlations while reducing their coherence. In contrast, for two-point density correlations, the initial ballistic propagation regime gives way to diffusion at intermediate times. Numerical simulations, based on a time-dependent matrix product state algorithm, are supplemented by a quantitatively accurate fermionic quasi-particle approach providing an intuitive description of the initial dynamics in terms of holon and doublon excitations.