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Corroborating the bulk-edge correspondence in weakly interacting one-dimensional topological insulators

2019; American Physical Society; Volume: 100; Issue: 7 Linguagem: Inglês

10.1103/physrevb.100.075114

2469-9977

Antonio Zegarra, Denis R. Candido, J. Carlos Egues, Wei Chen,

Quantum many-body systems

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using the interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a $T$-matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit.