Symmetry-enforced many-body separability transitions

• URL: http://arxiv.org/abs/2310.07286v2
• Date: Mon, 6 May 2024 01:47:42 GMT
• Title: Symmetry-enforced many-body separability transitions
• Authors: Yu-Hsueh Chen, Tarun Grover,
• Abstract summary: We study quantum many-body mixed states with a symmetry from the perspective of separability. We provide evidence for'symmetry-enforced separability transitions' in a variety of states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study quantum many-body mixed states with a symmetry from the perspective of separability, i.e., whether a mixed state can be expressed as an ensemble of short-range entangled (SRE) symmetric pure states. We provide evidence for 'symmetry-enforced separability transitions' in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric SRE pure states, while in the other regime, such a representation is not feasible. We first discuss Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next, we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternate perspective on recently discussed 'average SPT order'. We also study decohered p+ip superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of non-chiral states, while a fermion-parity preserving decoherence results in a phase transition at a non-zero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy NLTS (no low-energy trivial state) property, such as the recently discovered good LDPC codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition.

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