Building crystalline topological phases from lower-dimensional states

2017/05/31 by Sheng-Jie Huang, Hao Song, Yi-Ping Huang +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Combinatorics #Conjecture #Constraint (computer-aided design) #Geometry #Invertible matrix #Mathematics #Physics #Pure mathematics #Quantum many-body systems #Simple (philosophy) #Symmetry (geometry) #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #Type (biology) #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.96.205106

published as Phys. Rev. B 96, 205106 (2017) · 18+14 pages. S.-J.H. and H.S. are co-first-authors. v2: published version

openalex publication_date 2017/11/06 · arxiv created 2017/12/19 · arxiv updated 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Topological phases protected by the geometrical symmetries of crystal lattices turn out to be surprisingly simple. They can be built from simpler lower-dimensional states, arranged in a crystalline pattern.

Citations

• Interaction-enabled topological crystalline phases
• Space group symmetries and low lying excitations of many-body systems at integer fillings
• Periodic table for topological insulators and superconductors
• Lieb-Schultz-Mattis in higher dimensions
• 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 Insulators
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Two soluble models of an antiferromagnetic chain
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
• International Tables for Crystallography
• Ground state degeneracy in quantum spin systems protected by crystal symmetries

Cited by

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