Protected edge modes without symmetry

By Michael Levin. 2013

213 citations recorded by the source corpus.

We discuss the question of when a gapped 2D electron system without any symmetry has a protected gapless edge mode. While it is well known that systems with a nonzero thermal Hall conductance, $K_H \neq 0$, support such modes, here we show that robust modes can also occur when $K_H = 0$ -- if the system has quasiparticles with fractional statistics. We show that some types of fractional statistics are compatible with a gapped edge, while others are fundamentally incompatible. More generally, we give a criterion for when an electron system with abelian statistics and $K_H = 0$ can support a gapped edge: we show that a gapped edge is possible if and only if there exists a subset of quasiparticle types $M$ such that (1) all the quasiparticles in $M$ have trivial mutual statistics, and (2) every quasiparticle that is not in $M$ has nontrivial mutual statistics with at least one quasiparticle in $M$. We derive this criterion using three different approaches: a microscopic analysis of the edge, a general argument based on braiding statistics, and finally a conformal field theory approach that uses constraints from modular invariance. We also discuss the analogous result for 2D boson systems.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/0ba402559d50d8a350bacdfa404f819924650a9a

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Juven C. Wang
2. E. Witten
3. Ryan Thorngren
4. Liang Kong
5. X. Wen
6. Yifan Wang
7. D. Gaiotto
8. Yuji Tachikawa

In Condensed Matter Physics

1. Liang Kong
2. E. Witten
3. Juven C. Wang
4. Ryan Thorngren
5. Yifan Wang
6. X. Wen
7. D. Gaiotto
8. M. B. Hastings

Citations in the corpus

• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “Again, this unique gapped interface is also realized and consistent with earlier work [66–69].”
• Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, unknown): “A Lagrangian subgroup A is a subset of Abelian bosons in the topological order that are closed under fusion, have trivial mutual statistics, and that every other anyon braids non-trivially with at least one of the anyons in the subgroup[77, 78].”
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “See [13,14,21,30,35,38] for various perspectives on this problem.”
• Anyon condensation and tensor categories (2013, methodology): “e quadratic form, there is a one-to-one correspondence between Lagrangian algebras in the category C(G,q) and Lagrangian subgroups of G[FSV1, Thm.5.5]. So in this case, we recover the result in [KaS1][L][BJQ]. Remark 5.4. By the folding trick, a domain wall between a C-phase and a Dphase can be view”