Header

UZH-Logo

Maintenance Infos

Higher-order symmetry-protected topological states for interacting bosons and fermions


You, Yizhi; Devakul, Trithep; Burnell, F J; Neupert, Titus (2018). Higher-order symmetry-protected topological states for interacting bosons and fermions. Physical review. B, 98(23):235102.

Abstract

Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges. Here, we explore symmetry-protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher-order symmetry-protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the nontrivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.

Abstract

Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges. Here, we explore symmetry-protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher-order symmetry-protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the nontrivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.

Statistics

Citations

Dimensions.ai Metrics
21 citations in Web of Science®
20 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

31 downloads since deposited on 25 Jan 2019
18 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Electronic, Optical and Magnetic Materials
Physical Sciences > Condensed Matter Physics
Language:English
Date:3 December 2018
Deposited On:25 Jan 2019 13:43
Last Modified:29 Jul 2020 09:10
Publisher:American Physical Society
ISSN:2469-9950
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1103/physrevb.98.235102
Project Information:
  • : FunderSNSF
  • : Grant ID200021_169061
  • : Project TitleAnyons in topological matter: From axiomatic field theory to advanced materials

Download

Hybrid Open Access

Download PDF  'Higher-order symmetry-protected topological states for interacting bosons and fermions'.
Preview
Content: Published Version
Filetype: PDF
Size: 2MB
View at publisher