Irreducible Projective Representations and Their Physical Applications

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.

41 pages, 1 figure

References in corpus (10)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
• Quantum Bochner's theorem for phase spaces built on projective representations
• Casimir energy between two parallel plates and projective representation of Poincaré group

Cited by in corpus (14)

• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Enumeration and representation theory of spin space groups
• Enumeration of spin-space groups: Towards a complete description of symmetries of magnetic orders
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
• Symmetry-protected Nodal Points and Nodal Lines in Magnetic Materials
• Klein-bottle quadrupole insulators and Dirac semimetals
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups
• Fate of symmetry protected coherence in open quantum system
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• One-dimensional symmetric phases protected by frieze symmetries
• Threefold Way for Typical Entanglement
• Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux