Topological Green's function zeros in an exactly solved model and beyond

Abstract

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green's function and show that {in this model} they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite ``lifetime''. We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green's function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross-pollination between solid-state theory, high-energy physics and quantum information science.

5 papges, 9 pages supplement, 5 figures

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Cited by in corpus (10)

• Fermi-liquid corrections to the intrinsic anomalous Hall conductivity of topological metals
• The Weyl-Mott point: topological and non-Fermi liquid behavior from an isolated Green's function zero
• Probing Green's Function Zeros by Co-tunneling through Mott Insulators
• Quantum Restored Symmetry Protected Topological Phases
• Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Topological strongly correlated phases in orthorhombic diamond lattice compounds
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Robust boundary Luttinger surfaces in topological band structures
• Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems