Interacting topological quantum chemistry of Mott atomic limits

TL;DR

This paper extends topological quantum chemistry to interacting systems by introducing Mott atomic limits, enabling classification of symmetry-protected topological states using Green's functions, with comprehensive 1D classifications and numerical examples.

Contribution

It develops a novel framework for classifying interacting topological states via Green's functions, generalizing atomic limits to Mott atomic limits.

Findings

Classifies Mott atomic limit states in one dimension.

Provides numerical results on model systems.

Establishes a new classification scheme for interacting topological states.

Abstract

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles calculations, a band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals on the respective crystal lattice, or it is topological. For interacting systems, there is no single-particle band structure and hence, the TQC machinery grinds to a halt. We develop a framework analogous to TQC, but employing $n$-particle Green's function to classify interacting systems. Fundamentally, we define a class of interacting reference states that generalize the notion of atomic limits, which we call Mott atomic limits, and are symmetry protected topological states. Our formalism allows to fully classify these reference states (with $n=2$), which can themselves represent symmetry protected topological states. We present a comprehensive classification of such states in one-dimension and provide numerical results on model systems. With this, we establish Mott atomic limit states as a generalization of the atomic limits to interacting systems.