Topological phases with average symmetry

Lunch will be provided at 12:00pm, so please come early to eat mingle and eat lunch before the talk begins.

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Abstract: Topological phases are often defined in the presence of certain symmetries. In this talk I will show that topological phases are also well defined for average symmetries — symmetries that are only preserved upon ensemble averaging. In particular, I will introduce the notion of average symmetry-protected topological (ASPT) phases in two physically different settings: (1) disordered Hamiltonian systems at zero temperature, and (2) open quantum systems subject to decoherence. I will discuss some universal properties of ASPT phases and show how the story is different from the standard topological phases. We also generalize t’Hooft anomaly to average symmetries and use it to characterize nontrivial boundary states of ASPT.