# Revealing the nature of non-equilibrium phase transitions with quantum trajectories

## TL;DR

This paper uses quantum state diffusion to analytically study non-equilibrium phase transitions in a driven, damped collective spin system, providing exact results and insights into phase behavior and critical phenomena.

## Contribution

It offers a mostly analytical, finite-size defect-free analysis of non-equilibrium quantum phase transitions using quantum trajectories, revealing phase symmetry breaking and critical exponents.

## Key findings

- Exact critical exponents determined
- Finite size scaling analyzed
- Non-algebraic transition behavior explained

## Abstract

A damped and driven collective spin system is analyzed by using quantum state diffusion. This approach allows for a mostly analytical treatment of the investigated non-equilibrium quantum many body dynamics, which features a phase transition in the thermodynamical limit. The exact results obtained in this work, which are free of any finite size defects, provide a complete understanding of the model. Moreover, the trajectory framework gives an intuitive picture of the two phases occurring, revealing a spontaneously broken symmetry and allowing for a qualitative and quantitative characterization of the phases. We determine exact critical exponents, investigate finite size scaling, and explain a remarkable non-algebraic behaviour at the transition in terms of torus hopping.