Elementary band representations for the single-particle Green's function of interacting topological insulators

2021/03/31 by Dominik Lessnich, Dominik Leßnich, Stephen M. Winter +3
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Function (biology) #Geology #Graphene research and applications #Mathematics #Particle (ecology) #Physics #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.104.085116

published as Phys. Rev. B 104, 085116 (2021) · 12 pages, 6 figures

openalex publication_date 2021/08/11 · arxiv created 2021/08/30 · arxiv updated 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We discuss the applicability of elementary band representations (EBRs) to diagnose spatial- and time-reversal-symmetry protected topological phases in interacting insulators in terms of their single-particle Green's functions. We do so by considering an auxiliary noninteracting system H_T(k)=\ensuremath-G^\ensuremath-1(0,k), known as the topological Hamiltonian, whose bands can be labeled by EBRs. This labeling is robust if neither (i) the gap in the spectral function at zero frequency closes, (ii) the Green's function has a zero at zero frequency, or (iii) the Green's function breaks a protecting symmetry. We demonstrate the use of EBRs applied to the Green's function on the one-dimensional Su-Schrieffer-Heeger model with Hubbard interactions, which we solve by exact diagonalization for a finite number of unit cells. Finally, the use of EBRs for the Green's function to diagnose so-called symmetry-protected topological phases is discussed, but remains an open question.

Citations

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