Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model

TL;DR

This paper demonstrates that strong interactions in the Haldane model at quarter filling induce a ferromagnetic topological Mott insulator with a non-zero Chern number, expanding topological classification to correlated systems.

Contribution

It introduces a novel topological phase in the interacting Haldane model at quarter filling, showing the emergence of a ferromagnetic topological Mott insulator with a Chern number of one.

Findings

Large interactions induce a topological Mott insulator.

The phase exhibits ferromagnetism and non-zero Chern number.

Results are confirmed analytically and numerically.

Abstract

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically non-trivial Haldane model, we show that a quarter-filled state emerges with a non-zero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid state systems are discussed.