A solvable model for strongly interacting nonequilibrium excitons

TL;DR

This paper introduces an exactly solvable model for driven-dissipative excitons in a Bose-Hubbard system, revealing non-thermal steady-states and altered phase transition behavior in nonequilibrium conditions.

Contribution

It derives a closed-form steady-state solution for a driven-dissipative Bose-Hubbard model with all-to-all hopping, applicable to exciton systems and quantum simulators.

Findings

Steady-state solutions are obtainable analytically in certain limits.

The nonequilibrium phase diagram resembles the equilibrium one.

Steady-states are non-thermal, with modified phase transition characteristics.

Abstract

We study the driven-dissipative Bose-Hubbard model with all-to-all hopping and subject to incoherent pumping and decay, as is naturally probed in several recent experiments on excitons in WS2/WSe2 moir\'e systems, as well as quantum simulators. By positing a particular form of coupling to the environment, we derive the Lindblad jump operators and show that, in certain limits, the system admits a closed-form expression for the steady-state density matrix. Away from the exactly solvable regions, the steady-state can be obtained numerically for 100s-1000s of sites. We study the nonequilibrium phase diagram and phase transitions, which qualitatively matches the equilibrium phase diagram, agreeing with the intuition that increasing the intensity of the light is equivalent to changing the bosonic chemical potential. However, the steady-states are far from thermal states and the nature of the phase transitions is changed.