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Generalized symmetry-protected topological phases in mixed states from gauging dualities

Linhao Li, Zhen Bi, Weiguang Cao

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.

Generalized symmetry-protected topological phases in mixed states from gauging dualities

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 , including phases that are intrinsic to mixed states, and characterize them via string order parameters and protected edge modes.
Paper Structure (27 sections, 115 equations, 4 figures, 1 table)

This paper contains 27 sections, 115 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Group symmetries in open quantum systems
  4. Mixed-state phases
  5. Noninvertible symmetry from duality
  6. Dipole symmetry from duality
  7. Classification of $(1+1)d$ Rep($D_{2m})$ average SPT
  8. Rep($D_{2m})$ symmetry in open quantum systems
  9. Gauging as a one-to-one mapping between mixed-state phases
  10. Classification of Rep($D_{4n}$) ANISPT
  11. Lattice models of non-intrinsic Rep$(D_{8})$ ANISPT
  12. Trivial Rep$(D_{8})$ ANISPT phase
  13. Even and odd Rep$(D_{8})$ ANISPT phases
  14. Lattice models of Rep$(D_{8})$ IANISPT phase
  15. Fixed-point wavefunction
  16. ...and 12 more sections

Figures (4)

  • Figure 1: Illustration of gauging-based method to study ASPT phases from group SSB phases. The strong and weak conditions of symmetry operators are shown in \ref{['eq: symmetry conditions-1']} and \ref{['eq: symmetry conditions-2']}.
  • Figure 2: The Phase diagram of model with Hamiltonian \ref{['eq: SSB Hal']} and channel \ref{['eq:quantumchannel']} before gauging and the phase diagram of the model with Hamiltonian \ref{['eq: dual Hal']} and channel \ref{['eq: dual channel']} after gauging.
  • Figure 3: The Phase diagram of model with Hamiltonian \ref{['eq: SSB HAL2']} and channel \ref{['eq:quantumchannel']} before gauging and the phase diagram of the model with Hamiltonian \ref{['eq: even HAL']} and channel \ref{['eq: dual channel']} after gauging.
  • Figure 4: The phase diagram of model \ref{['eq: dual Hal app']}.