Frequency domain winding number and interaction effect on topological insulators

TL;DR

This paper investigates how interactions affect topological insulators in 3D and 4D, revealing that interactions can induce nontrivial frequency-domain winding numbers and alter topological classes without long-range order.

Contribution

It introduces a method to analyze interaction effects on topological indices using Green's functions and shows that interactions can change topological phases without symmetry breaking.

Findings

Interactions induce nontrivial frequency-domain winding numbers.

Topological classes can change due to interactions without long-range order.

Practical methods for frequency-momentum integration in Green's function calculations.

Abstract

We study the effect of interactions on the time reversal invariant topological insulators in four and three spatial dimensions. Their topological indices are expressed by the interacting Green's functions. Under the local self-energy approximation, we find that interaction could induce nontrivial frequency-domain winding numbers and change the topological classes of the system. Our results suggest that the topological phases could be destroyed without developing long range orders. Practical issues on the accurate frequency-momentum integration combined with DMFT and diagrammatic calculations of the interacting Green's functions are also addressed.