Universal symmetry-protected topological invariants for symmetry-protected topological states

2013/11/30 by Ling-Yan Hung, Xiao-Gang Wen · 1 citation
Mathematics · Physics and Astronomy · #Cohomology #Combinatorics #Computer science #Geometry #Group (periodic table) #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Space (punctuation) #Symmetry (geometry) #Symmetry group #Symmetry protected topological order #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.89.075121

published as Phys. Rev. B 89, 075121 (2014) · 12 pages, 11 figures. Added references

openalex publication_date 2014/02/19 · arxiv created 2014/05/30 · arxiv updated 2014/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Symmetry-protected topological (SPT) states are short-range entangled states with a symmetry G. They belong to a new class of quantum states of matter which are classified by the group cohomology H^d+1(G,ℝ/ℤ) in d-dimensional space. In this paper, we propose a class of symmetry-protected topological invariants that may allow us to fully characterize SPT states with a symmetry group G [i.e., allow us to measure the cocycles in H^d+1(G,ℝ/ℤ) that characterize the SPT states]. We give an explicit and detailed construction of symmetry-protected topological invariants for 2+1D SPT states. Such a construction can be directly generalized to other dimensions.

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