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

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.

To appear in PRR Letter. 7 pages, 2 figures + Supplemental Material

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• Fermi and Luttinger arcs: two concepts, realized on one surface
• Topological Green's function zeros in an exactly solved model and beyond
• Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model
• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
• Fermi-liquid corrections to the intrinsic anomalous Hall conductivity of topological metals
• Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
• The Weyl-Mott point: topological and non-Fermi liquid behavior from an isolated Green's function zero
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Engineering correlated Dirac fermions and flat bands on SiC with transition-metal adatom lattices
• Correlated Hopf insulators