# A solvable family of driven-dissipative many-body systems

## TL;DR

This paper introduces a family of non-equilibrium, dissipative many-body models that are exactly solvable across dimensions, enabling new insights into steady states and decoherence effects relevant for quantum systems.

## Contribution

It presents a class of non-equilibrium models analogous to the transverse-field Ising model that are exactly solvable, and uses these solutions to analyze phase transitions and decoherence in quantum systems.

## Key findings

- Broad class of models solvable in any dimension
- Proved a no-go theorem on steady-state phase transitions
- Analyzed decoherence effects in quantum computing architectures

## Abstract

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of non-equilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.