Topologically Ordered Steady States in Open Quantum Systems

TL;DR

This paper explores steady-state topological order in open quantum systems, demonstrating its stability in three dimensions and identifying universal features like emergent gauge fields and defect dynamics.

Contribution

It constructs exactly solvable models showing the stability of steady-state topological degeneracy in 3D and analyzes the transition to trivial phases.

Findings

Steady-state topological degeneracy is stable in 3D but fragile in 2D.

Universal features include emergent gauge fields and slow defect relaxation.

Numerical simulations reveal phase transitions from topologically ordered to trivial states.

Abstract

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.