Magnetic Order Driven Topological Transition in the Haldane-Hubbard Model

TL;DR

This paper investigates how magnetic order influences topological phase transitions in the Haldane-Hubbard model, revealing scenarios where magnetic interactions induce continuous or first-order topological transitions, relevant to cold atom experiments.

Contribution

It introduces a mean-field framework linking magnetic order to topological transitions and explores beyond mean-field effects, identifying multiple transition scenarios in the Haldane-Hubbard model.

Findings

Magnetic order modifies topological parameters in the Haldane model.

Topological transitions can be continuous with gap closing or first-order with gap opening.

Both transition scenarios are present in the phase diagram of the Haldane-Hubbard model.

Abstract

In this letter we study the Haldane model with on-site repulsive interactions at half-filling. We show that the mean-field Hamiltonian with magnetic order effectively modifies parameters in the Haldane Hamiltonian, such as sublattice energy difference and phase in next nearest hopping. As interaction increases, increasing of magnetic order corresponds to varying these parameters and consequently, drives topological transitions. At the mean-field level, one scenario is that the magnetic order continuously increases, and inevitably, the fermion gap closes at the topological transition point with nonzero magnetic order. Beyond the mean-field, interaction between fermions mediated by spin-wave fluctuations can further open up the gap, rendering a first-order transition. Another scenario is a first-order transition at mean-field level across which a canted magnetic order develops discontinuously, avoiding the fermion gap closing. We find that both scenarios exist in the phase diagram of the Haldane-Hubbard model. Our predication is relevant to recent experimental realization of the Haldane model in cold atom system.