Mixed-state Topological Order in (2+1)d

Abstract: Ground states of gapped local Hamiltonians can be classified, up to quasi-local unitary equivalence, by their underlying topological order. In 2+1 dimensions, it is widely believed—and in some cases rigorously established—that topological orders are fully characterized by their topological line operators that generate 1-form symmetries, up to stacking with invertible states. Mathematically, the topological line operators form a modular tensor category.

In this talk, I will discuss recent progress on extending this framework to many-body mixed states. I will begin by reviewing the ground-state classification, the role of 1-form symmetries, and the physics of decohered topological states. I will then argue that, under an appropriate notion of equivalence for mixed states, (2+1)d mixed-state topological order is (partially) classified by premodular categories.

condensed mattergeneral relativity and quantum cosmologyHEP - latticeHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

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Quantum Theories of Fields, Matter, and Strings

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