Phase diagram topology of the Haldane-Hubbard-Coulomb model

TL;DR

This paper uses Diagrammatic Monte Carlo to accurately map the phase diagram of the Haldane-Hubbard-Coulomb model, revealing the importance of momentum-dependent self-energy and the impact of long-range interactions on topological phase transitions.

Contribution

It provides the first precise phase diagram of the model considering both on-site and long-range Coulomb interactions, highlighting the significance of momentum dependence in self-energy calculations.

Findings

Accurate phase transition points identified using Diagrammatic Monte Carlo.

Long-range interactions significantly shift topological phase boundaries.

Momentum dependence of self-energy is crucial for correct phase diagram mapping.

Abstract

We study the phase diagram of the interacting spin-$1/2$ Haldane model with chiral phase $\phi = \pi/2$ at half-filling. Both on-site and long-range Coulomb repulsive interactions (Haldane-Hubbard-Coulomb model) are considered. The problem with on-site interaction $U$ alone was addressed in the past by a variety of approximate and finite size methods that produced results in disagreement with each other both quantitatively and qualitatively. Here we employ the Diagrammatic Monte Carlo technique to accurately locate phase transition points to the topologically nontrivial phases in the $(\Delta, U)$-plane, where $\pm \Delta$ is the inversion symmetry breaking on-site energy, and establish that momentum dependence of self-energy cannot be neglected in the proper treatment. We also find that even modest long-range interactions, typically discarded in theoretical considerations, result in significant shifts of transition lines.