Bulk-Boundary Correspondence for Three-Dimensional Symmetry-Protected Topological Phases

2015/12/30 by Chenjie Wang, Chien-Hung Lin, Michael Levin · 60 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Boundary (topology) #Combinatorics #Geometry #Mathematical analysis #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Symmetry (geometry) #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevx.6.021015

published in Physical Review X 6(2) (American Physical Society) · 31 pages, 14 figures, 1 table

arxiv created 2015/12/30 · openalex publication_date 2016/05/09 · arxiv updated 2016/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Linking the properties of a material's bulk and surface is often challenging and limited to low-dimensional systems. Now, researchers theoretically demonstrate a bulk-boundary correspondence for a class of three-dimensional insulators, namely symmetry-protected topological phases of matter.

Citations

• Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
• Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Topological insulators and superconductors
• Entanglement spectrum of a topological phase in one dimension
• Topological invariants for gauge theories and symmetry-protected topological phases
• Topological Insulators
• Classification of gapped symmetric phases in one-dimensional spin systems
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• An introduction to lattice gauge theory and spin systems
• Anyons in an exactly solved model and beyond
• Anomalies of discrete symmetries in various dimensions and group cohomology

Cited by

• Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries