Speaker: Tyler Ellison (Yale)
Title: Towards a classification of mixed-state topological orders in two spatial dimensions
Abstract: The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment is inevitable — thus motivating the investigation of topological orders in the context of mixed states. In this work, we take a step toward classifying mixed-state topological orders in two spatial dimensions by considering their (emergent) generalized symmetries. We argue that their 1-form symmetries and the associated anyon theories lead to a partial classification under two-way connectivity by quasi-local quantum channels. This allows us to establish the existence of mixed-state topological orders that are intrinsically mixed, i.e., that have no ground state counterpart. We discuss a wide range of examples based on incoherently proliferating anyons, "classically gauging" symmetry-enriched topological orders, and decohering Walker-Wang models. Based on our examples, we identify two possible effects of quasi-local quantum channels on the anyon theories: (1) through the incoherent proliferation of anyons — the anyon theory can be reduced to the commutant of the proliferated anyons, or (2) classical gauging can result in the symmetrization of anyons and an extension by transparent bosons. Given these two mechanisms, we conjecture that mixed-state topological orders are classified by premodular anyon theories, i.e., those for which the braiding relations may be degenerate.
This talk is based on arXiv:2405.02390, done in collaboration with Meng Cheng.