Yuan-Ming Lu

Symmetry-protected topological phases from decorated domain walls

Symmetry-protected topological phases generalize the notion of topological insulators to strongly interacting systems of bosons or fermions. A sophisticated group cohomology approach has been used to classify bosonic symmetry-protected topological phases, which however does not transparently predict their properties. Here we provide a physical picture that leads to an intuitive understanding of a large class of symmetry-protected topological phases in d=1,2,3 dimensions. Such a picture allows us to construct explicit models for the symmetry-protected topological phases, write down ground state wave function and discover topological properties of symmetry defects both in the bulk and on the edge of the system. We consider symmetries that include a Z2 subgroup, which allows us to define domain walls. While the usual disordered phase is obtained by proliferating domain walls, we show that symmetry-protected topological phases are realized when these domain walls are decorated, that is, are themselves symmetry-protected topological phases in one lower dimension. This construction works both for unitary Z2 and anti-unitary time reversal symmetry.

Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to Z 2 spin liquids

We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a

Measuring space-group symmetry fractionalization in Z 2 spin liquids

K

Unification of bosonic and fermionic theories of spin liquids on the kagome lattice

-matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying

Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach

{Z}_{2}

Erratum: Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach [Phys. Rev. B86, 125119 (2012)]

topological order (

Topological phase transition in a bilaer toric code model

{Z}_{2}

Measuring symmetry fractionalization in topological orders: application to Z2 spin liquids on kagome lattice

spin liquids) in the presence of an internal

of bosonic and fermionic theories of spin liquids on the kagome lattice

{Z}_{2}

Effective field theory, edge states and classification of symmetric Z2 spin liquids

global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.