Topological Green function of interacting systems

Abstract

We construct a Green function, which can identify the topological nature of interacting systems. It is equivalent to the single-particle Green function of effective non-interacting particles, the Bloch Hamiltonian of which is given by the inverse of the full Green function of the original interacting particles at zero frequency. The topological nature of the interacting insulators is originated from the coincidence of the poles and the zeros of the diagonal elements of the constructed Green function. The cross of the zeros in the momentum space closely relates to the topological nature of insulators. As a demonstration, using the zero's cross, we identify the topological phases of magnetic insulators, where both the ionic potential and the spin exchange between conduction electrons and magnetic moments are present together with the spin-orbital coupling. The topological phase identification is consistent with the topological invariant of the magnetic insulators. We also found an antiferromagnetic state with topologically breaking of the spin symmetry, where electrons with one spin orientation are in topological insulating state, while electrons with the opposite spin orientation are in topologically trivial one.

arXiv commentupdated reference and corrected figures

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Cited by in corpus (6)

• Unified role of Green's function poles and zeros in topological insulators
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Zeros of Green Functions in Topological Insulators
• Quasiparticle picture of topological phase transitions induced by interactions
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates