Topological Diagnosis of Strongly Correlated Electron Systems

TL;DR

This paper introduces a novel framework using Green's function Berry curvature to diagnose topology in strongly correlated electron systems, exemplified by Mott insulators, enabling the discovery of topological materials in complex quantum phases.

Contribution

It develops a general method to identify topology in strongly correlated systems via Green's function zeros and flux quantization, advancing the diagnosis of topological phases in Mott insulators.

Findings

Green's function Berry flux of zeros is quantized.

Framework applies to symmetry-protected nodes in bandstructure.

Enables search for topological materials with strong correlations.

Abstract

The intersection of electronic topology and strong correlations offers a rich platform to discover exotic quantum phases of matter and unusual materials. An overarching challenge that impedes the discovery is how to diagnose topology in strongly correlated settings, as exemplified by Mott insulators. Here, we develop a general framework to address this outstanding question and illustrate its power in the case of Mott insulators. The concept of Green's function Berry curvature -- which is frequency dependent -- is introduced. We apply this notion in a system that contains symmetry-protected nodes in its noninteracting bandstructure; strong correlations drive the system into a Mott insulating state, creating contours in frequency-momentum space where the Green's function vanishes. The Green's function Berry flux of such zeros is found to be quantized, and is as such direct probe of the system's topology. Our framework allows for a comprehensive search of strongly correlated topological materials with Green's function topology.