2018/10/31 by Ranjith Kumar R, Sujit Sarkar
Mathematics · Physics and Astronomy · #Geometry #Global symmetry #Hamiltonian (control theory) #Mathematics #Mesoscopic physics #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Quantum mechanics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Symmetry number #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.1080/01411594.2020.1723588
published as Phase Transitions, 93:3, 287-300 (2020) · Extensively revised version with a few new interpretations of calculations. Comments will be very much appreciated
arxiv created 2019/07/24 · openalex created_date 2019/07/30 · crossref issued 2020/02/05 · crossref published 2020/02/05 · crossref published-online 2020/02/05 · openalex publication_date 2020/02/05 · crossref created 2020/02/06 · crossref deposited 2020/02/26 · crossref published-print 2020/03/03 · arxiv updated 2021/01/18 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/05
Symmetry plays an important role in the topological states of quantum matter. Cartan found three symmetry classes, Altland and Zirnbauer extended it to the 10-fold symmetry class for mesoscopic systems. We observe the emergence of a new symmetry class for BdG Hamiltonians. This new symmetry class appears for the BdG Hamiltonian in spinful background. We also observe the interesting feature that there is no evidence of Kramers's degeneracy for this BdG model Hamiltonian either in spinless or in spinful background. We call the extra symmetry class X, i.e. expanding the 10-fold symmetry classes for topological states of quantum matter. These BdG Hamiltonians show many new, interesting and insightful results.