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Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States | | Tsuf Lichtman
; Ryan Thorngren
; Netanel H. Lindner
; Ady Stern
; Erez Berg
; | | Date: |
9 Mar 2020 | | Abstract: | We study quasi-1d systems that emerge at the edge of a topologically ordered
state, or at the boundary between two topologically ordered states. We argue
that anyons of the bulk are associated with emergent symmetries of the quasi-1d
system, which play a crucial role in the structure of its phase diagram. Using
this symmetry principle, anyon condensation transitions at the boundaries of
Abelian states can be understood in terms of symmetry breaking or symmetry
protected topological transitions. Yet more exotic phenomena occur when the
bulk hosts non-Abelian anyons. To demonstrate these principles, we explore the
phase diagrams of the edges of a single and a double layer of the toric code,
as well as those of domain walls in a single and double-layer Kitaev spin
liquid (KSL). In the case of the KSL, we find that the presence of a
non-Abelian anyon in the bulk enforces Kramers-Wannier self-duality as a
symmetry of the effective boundary theory. These examples illustrate a number
of surprising phenomena, such as spontaneous duality-breaking, two-sector phase
transitions, and unfreezing of marginal operators at a transition between
different gapless phases. | | Source: | arXiv, 2003.4328 | | Services: | Forum | Review | PDF | Favorites | |
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