Interacting Chern Insulator in Infinite Spatial Dimensions

TL;DR

This paper explores a high-dimensional Chern insulator with interactions, revealing a rich phase diagram with many topologically distinct phases and introducing a non-quantized Chern density as a key topological marker.

Contribution

It extends the study of Chern insulators to infinite dimensions, demonstrating the model's well-defined nature and revealing a continuum of topological phases with novel features.

Findings

Existence of a continuum of topologically distinct phases

Introduction of a non-quantized Chern density in infinite dimensions

Unconventional features in insulating and semi-metal states

Abstract

We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well-defined and nontrivial in the $D \to \infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semi-metal states, which are unconventional already in the non-interacting case. Topological phases are characterized by a non-quantized Chern density replacing the Chern number as $D\to \infty$.