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2025

Topological Mixed States: Phases of Matter from Axiomatic Approaches

Yang, Tai-Hsuan, Shi, Bowen, Lee, Jong Yeon

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For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians.

The generalization of this conceptual paradigm to open quantum systems, however, remains elusive, often relying on operational definitions without fundamental principles.
Here, we fill this gap by proposing an approach based on three axioms: ($i$) local recoverability, ($ii$) absence of long-range correlations, and ($iii$) spatial uniformity.
States that satisfy these axioms are fixed points; requiring the axioms only after coarse-graining promotes each fixed point to an equivalence class, i.e., a phase, presenting the first step towards the axiomatic classification of mixed-state phases of matter: mixed-state bootstrap program.

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