期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 51, 期 2, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aa971a
关键词
eigenfunction method; projective representations; anti-unitary group; class operator
资金
- Ministry of Science and Technology of China [2016YFA0300504]
- Research Funds of Renmin University of China [15XNLF19]
- MOST of the National Key Basic Research Program of China [2013CB922004]
- NSFC [91421305]
- National Basic Research Program of China [2015CB921104]
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.
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