Topological Green function of interacting systems

TL;DR

This paper introduces a Green function method to identify the topological phases of interacting systems, linking zeros and poles of the Green function to topological properties, and demonstrates its effectiveness on magnetic insulators.

Contribution

It develops a Green function framework that characterizes topological phases in interacting systems through zeros and poles analysis, extending topological classification methods.

Findings

Identified topological phases of magnetic insulators using zeros of Green function.

Discovered an antiferromagnetic state with spin-dependent topological properties.

Validated the method's consistency with known topological invariants.

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.