Illinois Physicists Propose Framework for Classifying Non-Equilibrium Quantum Phases

Illinois physicists at the Anthony J. Leggett Institute for Condensed Matter Theory have proposed a new framework for classifying non-equilibrium quantum phases of matter, published in Physical Review X. This work addresses the challenges of categorizing open quantum systems, which interact freely with their environment, and overcomes limitations of existing classification methods.

The researchers introduced three axioms: local recoverability, absence of long-range correlations, and spatial uniformity. States satisfying these axioms are considered fixed points, and the framework promotes these fixed points to equivalence classes, or phases. This marks a significant step towards a systematic classification of mixed-state phases of matter.

From these axioms, a rich set of topological data emerges, which is crucial for distinguishing between different mixed-state phases. The study reveals that each topological mixed state supports locally indistinguishable classical and/or quantum logical memories, responding uniquely to topological operations. Furthermore, the researchers identified a hierarchy of secret-sharing constraints in non-Abelian phases, where reliable recovery of information requires specific coordination among spatial subregions.

Large-scale numerical simulations were conducted to validate the stability of the proposed framework. The results showed that weakly decohered fixed points respect the axioms after coarse-graining, and the axiom violations exhibit a critical point crossing, facilitating its identification without ambiguity. These findings lay the groundwork for a comprehensive classification of topological states in open quantum systems.