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Physical Review B 105, 155112 (2022)

ISSN: 2469-9950, SCIE

Topological Green function of interacting systems

Minh-Tien Tran, Duong-Bo Nguyen, Hong-Son Nguyen, and Thanh-Mai Thi Tran

We construct a single-particle Green function, which can identify topological phases of interacting systems. The Green function is defined by an effective Bloch Hamiltonian, which is equal to the inverse of the full Green function of interacting particles at zero frequency. Topological phases of interacting systems can be detected by the coincidence of the poles and the zeros of the diagonal components of the constructed Green function. The crosses of the zeros in the momentum space are also a signal of nontrivial topological phases. As a demonstration, we identify the topological phases in a minimal model of magnetic insulators. The model describes the double exchange process between itinerant electrons and magnetic moments in the presence of the spin-orbital coupling and the ionic potential of the itinerant electrons. The identification of topological phases by the zero’s crosses is consistent with the topological invariant. 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.

DOI: https://doi.org/10.1103/PhysRevB.105.155112