Failure of Topological Invariants in Strongly Correlated Matter

Abstract

We show exactly that standard `invariants' advocated to define topology for non-interacting systems deviate strongly from the Hall conductance whenever the excitation spectrum contains zeros of the single-particle Green function, $G$, as in general strongly correlated systems. Namely, we show that if the chemical potential sits atop the valence band, the `invariant' changes without even accessing the conduction band but by simply traversing the band of zeros that might lie between the two bands. Since such a process does not change the many-body ground state, the Hall conductance remains fixed. This disconnect with the Hall conductance arises from the replacement of the Hamiltonian, $h(\bb k)$, with $G^{-1}$ in the current operator, thereby laying plain why perturbative arguments fail.

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Simplified topological invariants for interacting insulators
• Topological invariants and interacting one-dimensional fermionic systems
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Doped Mott Insulators Break ${\mathbb{Z}}_2$ Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points
• Interacting topological quantum chemistry of Mott atomic limits
• Exactly solvable model of Fermi arcs and pseudogap
• Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator

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• Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions
• Fermi and Luttinger arcs: two concepts, realized on one surface
• Topological Green's function zeros in an exactly solved model and beyond
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Correlated Topological Mixed-Valence Insulators in Moiré Hetero-Bilayers
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• 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
• Computing the ${\mathbb{Z}}_2$ Invariant in Two-Dimensional Strongly-Correlated Systems
• Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Probing Green's Function Zeros by Co-tunneling through Mott Insulators
• Incipient quantum spin Hall insulator under strong correlations
• Impact of correlations on topology in Kane-Mele model decorated with impurities
• 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
• Nematic order in topological SYK models
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Topological phase transition driven by Hatsugai-Kohmoto interaction on the Kagome lattice
• Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems
• Robust boundary Luttinger surfaces in topological band structures