Understand
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'.