Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros

TL;DR

This paper explores how symmetry constraints influence spectral crossings in a Mott insulator using Green's function zeros and poles, revealing new insights into topological states in strongly correlated systems.

Contribution

It demonstrates the application of symmetry constraints to Green's function zeros and poles in a Mott insulator, extending the framework to strongly interacting systems.

Findings

Green's function zeros and poles obey symmetry constraints.

Spectral crossings relate to degeneracies of non-interacting states.

Framework applies to strongly correlated topological materials.

Abstract

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original non-interacting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design.