# Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

## TL;DR

This paper reveals a symmetry in driven-dissipative Bose-Hubbard systems, showing that their steady states and phenomena like fermionization and superbunching are invariant under simultaneous sign changes of key parameters, enabling equivalent behaviors with attractive or repulsive interactions.

## Contribution

The study uncovers a fundamental symmetry in the Lindblad master equation for driven-dissipative Bose-Hubbard models, linking attractive and repulsive interaction regimes.

## Key findings

- Steady states are invariant under simultaneous sign change of parameters.
- Local boson number distribution and correlations are unchanged.
- Phenomena like fermionization and superbunching occur in both interaction regimes.

## Abstract

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions.