Topological phase transitions and universality in the Haldane-Hubbard model

TL;DR

This paper analyzes the Haldane-Hubbard model using exact Renormalization Group methods, revealing how weak interactions affect topological phase transitions, induce phase shifts, but preserve universal conductivity properties.

Contribution

It provides a rigorous construction of the topological phase diagram for weak interactions and demonstrates the universality of conductivity despite nontrivial renormalizations.

Findings

Interactions shift the topological transition line.

Intermediate phases are absent at weak coupling.

Conductivity remains universal at the critical line.

Abstract

We study the Haldane-Hubbard model by exact Renormalization Group techniques. We construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line. The presence of new intermediate phases, absent in the non interacting case, is rigorously excluded at weak coupling. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity do not depend on the interaction, thanks to remarkable cancellations due to lattice Ward Identities.