[论文解读] Generalized symmetry-protected topological phases in mixed states from gauging dualities

Linhao Li, Zhen Bi+1 more|arXiv (Cornell University)|Mar 18, 2026

Topological Materials and Phenomena被引用 0

一句话总结

该论文提出一个基于量纲估计的框架，用于在混态中对广义对称保护拓扑（ASPT）相进行分类，将不可逆和偶极ASPT相映射到对偶的普通对称分类，并在（1+1)d中构建晶格模型。

ABSTRACT

Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably noninvertible and dipole symmetries--have become powerful organizing principles for exotic quantum phases, yet their implications for mixed states remain less explored. In this work, we bridge these directions through a gauging correspondence between mixed-state phases with generalized symmetries and mixed-state phases with ordinary group symmetries, recasting the classification of noninvertible and dipole ASPT phases into familiar classifications of symmetry breaking and ASPT phases with dual symmetries. Using this approach, we classify and construct a subclass of ASPT phases with non-invertible and dipole symmetries in $(1+1)d$, including phases that are intrinsic to mixed states, and characterize them via string order parameters and protected edge modes.

研究动机与目标

• Motivate the study of topological phases in open quantum systems described by mixed states with strong and weak (average) symmetries.
• Introduce a gauging correspondence that relates mixed-state phases with generalized symmetries to those with ordinary group symmetries.
• Classify and construct a subclass of ASPT phases with noninvertible and dipole symmetries in (1+1)d, including intrinsic mixed-state ASPT phases.
• Characterize these phases using edge modes and string-order parameters, and provide a constructive scheme to prepare such states using finite-depth local circuits.

提出的方法

• Review strong/weak symmetry actions on density matrices in open quantum systems.
• Describe gauging as a finite-depth local quantum circuit operation that maps between mixed-state phases with generalized symmetries and those with dual group symmetries.
• Establish a two-way connectivity classification: mixed-state phases are two-way connected by locally symmetric finite-depth local channels (FDLCs).
• Apply gauging to map Rep(D2m) noninvertible/dipole cases to dual group-symmetry ASPT classifications.
• Provide explicit lattice realizations for Rep(D8) ANISPTs and analyze edge modes and string-order diagnostics.

实验结果

研究问题

• RQ1 Can mixed-state phases with noninvertible or dipole generalized symmetries be classified within the two-way connectivity framework?
• RQ2 How does gauging relate mixed-state ASPT phases with generalized symmetries to familiar classifications of symmetry-breaking and SPT phases under dual symmetries?
• RQ3 What lattice models realize Rep(D4n) ANISPTs in (1+1)d and what are their edge and bulk diagnostics?
• RQ4 When are generalized-symmetry ASPT phases intrinsic to mixed states (IASPT) versus inherited from pure-state counterparts?

主要发现

• A one-to-one correspondence is established between mixed-state phases protected by generalized symmetries and those protected by dual ordinary group symmetries via gauging.
• Classification of Rep(D4n) ANISPTs in (1+1)d reduces to symmetry-breaking and SPT classifications of the dual group, including intrinsic average ASPT phases.
• Explicit lattice constructions realize Rep(D8) ANISPTs and reveal edge-mode structure and string-order parameters.
• Intrinsic ANISPT (IASPT) exists for certain even/odd n cases, with some nonintrinsic ANISPTs (NANISPT) for others, tied to unbroken symmetry subgroups before gauging.
• Gauging procedures can be implemented by finite-depth circuits with ancillas and measurements, providing a constructive preparation scheme for mixed-state ASPT order.
• The framework clarifies when resulting generalized-symmetry ASPT phases are intrinsic to the mixed-state regime versus inherited from pure-state physics.