Symmetry Protected Topological Phases of Mixed States in the Doubled Space
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913374991810560 |
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| author | Ma, Ruochen Turzillo, Alex |
| author_facet | Ma, Ruochen Turzillo, Alex |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry Protected Topological Phases of Mixed States in the Doubled Space Ma, Ruochen Turzillo, Alex Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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. |
| title | Symmetry Protected Topological Phases of Mixed States in the Doubled Space |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.13280 |