Braiding statistics approach to symmetry-protected topological phases
read the original abstract
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase." We describe a simple physical construction that distinguishes this system from a conventional paramagnet: we couple the system to a Z_2 gauge field and then show that the \pi-flux excitations have different braiding statistics from that of a usual paramagnet. In addition, we show that these braiding statistics directly imply the existence of protected edge modes. Finally, we analyze a particular microscopic model for the edge and derive a field theoretic description of the low energy excitations. We believe that the braiding statistics approach outlined in this paper can be generalized to a large class of symmetry-protected topological phases.
This paper has not been read by Pith yet.
Forward citations
Cited by 5 Pith papers
-
Constructing Bulk Topological Orders via Layered Gauging
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
-
Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
-
Twisted quantum doubles are sign problem-free
Twisted quantum double phases for finite groups can be realized in sign problem-free local Hamiltonians via stochastic series expansion, contrary to the prior belief that non-positive wavefunctions imply an intrinsic ...
-
There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
-
Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.