# A solvable model for strongly interacting nonequilibrium excitons

## TL;DR

This paper introduces a solvable model to study nonequilibrium phase transitions in excitons formed in semiconductor bilayers under intense laser excitation.

## Contribution

The paper presents a novel solvable model for nonequilibrium excitons, capturing phase transitions in open quantum systems.

## Key findings

- The model shows a nonequilibrium phase transition out of the Mott insulator phase of excitons.
- The steady-state density matrix can be expressed in closed-form under certain conditions.
- Phase transitions in the model differ from thermal systems due to non-thermal steady states.

## Abstract

Excitons, bound states of electrons and holes, can be formed by shining a laser on a semiconductor. Recent experiments have suggested that sufficiently intense laser excitation applied to a WS2-WSe2 bilayer creates a “Mott insulator” of excitons in which they fill a lattice and can no longer easily move around. Since the excitons have a finite lifetime before decaying, this phase transition is fundamentally “nonequilibrium.” By developing a solvable toy model that goes beyond the standard approach of the literature, we theoretically study and characterize a nonequilibrium phase transition out of the Mott insulator phase and validate some of the experimental heuristics. The results provide a relevant exemplar of a phase transition in an open quantum system.

We study the driven-dissipative Bose-Hubbard model with an all-to-all hopping term in the system Hamiltonian, while subject to incoherent pumping and decay from the environment. This system is naturally probed in several recent experiments on excitons in WS2/WSe2 moiré 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 to 1,000s 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.