Symmetry Protected Topological Phases of Mixed States in the Doubled Space

2024/03/20 by Ruochen Ma, Ma, Ruochen, Alex Turzillo +1 · 17 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2403.13280

Abstract

The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen in pure states, mixed states can exhibit average symmetries—symmetries that act on component states while leaving the ensemble invariant. In this work, we systematically characterize symmetry-protected topological (SPT) phases of short-range entangled (SRE) mixed states of spin systems—protected by both average and exact symmetries—by studying their pure Choi states in a doubled Hilbert space, where the familiar notions and tools for SRE and SPT pure states apply. This advantage of the doubled space comes with a price: extra symmetries as well as subtleties around how hermiticity and positivity of the original density matrix constrain the possible SPT invariants. Nevertheless, the doubled-space perspective allows us to obtain a systematic classification of mixed-state SPT (MSPT) phases. We also investigate the robustness of MSPT invariants under symmetric finite-depth quantum channels, the bulk-boundary correspondence for MSPT phases, and the consequences of the MSPT invariants for the separability of mixed states and the symmetry-protected sign problem. In addition to MSPT phases, we study the patterns of spontaneous symmetry breaking (SSB) of mixed states, including the phenomenon of exact-to-average SSB, and the order parameters that detect them. Mixed-state SSB is related to an ingappability constraint on symmetric Lindbladian dynamics.

Cited by

• Edge bits in average symmetry protected topological mixed state
• Information dynamics and symmetry breaking in generic monitored ℤ₂-symmetric open quantum systems
• Localization and Delocalization of Quantum Trajectories in the Liouvillian Spectrum
• Holographic duality between bulk topological order and boundary mixed-state order
• Universal decay of (conditional) mutual information in gapped pure- and mixed-state quantum matter
• Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
• Succession of Ising criticality and its threshold in critical quantum Ising model subject to symmetric decoherence
• Simulation of bilayer Hamiltonians based on monitored quantum trajectories
• Equally entangled multiqubit states
• Symmetry enforces entanglement at high temperatures
• Defect Networks for Topological Phases Protected By Modulated Symmetries
• Quantum circuit complexity and unsupervised machine learning of topological order
• Absence of dissipation-free topological edge states in quadratic open fermions
• SymTFT Approach for Mixed States with Non-Invertible Symmetries
• The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs
• Mixed-state phases from local reversibility
• Detection of 2D SPT phases under decoherence

Related

• Diagnosing 2D symmetry protected topological states via mixed state anomaly
• Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space
• Detection of 2D SPT phases under decoherence
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic