Irreducible projective representations and their physical applications

2016/05/31 by Jian Yang, Zheng-Xin Liu · 14 citations
Physics and Astronomy · #Algebra over a field #Irreducible element #Irreducible representation #Lemma (botany) #Nuclear physics research studies #Physics of Superconductivity and Magnetism #Projective geometry #Projective test #Quantum many-body systems #Spectrum (functional analysis) #Symmetry (geometry) #Symmetry group #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1088/1751-8121/aa971a

published in Journal of Physics A Mathematical and Theoretical 51(2), 025207 (Institute of Physics) · 41 pages, 1 figure

openalex created_date 2016/06/24 · openalex publication_date 2017/10/31 · arxiv created 2017/12/16 · arxiv updated 2017/12/19 · openalex updated_date 2026/08/05

Abstract

Abstract An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.

Citations

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