Interacting topological quantum chemistry of Mott atomic limits

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.

References in corpus (26)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Calculations of Hubbard U from first-principles
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Magnetic Topological Quantum Chemistry
• Simplified topological invariants for interacting insulators
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• A polymorphous band structure model of gapping in the anti-ferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Geometric approach to fragile topology beyond symmetry indicators
• Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Topology invisible to eigenvalues in obstructed atomic insulators
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Identifying, and constructing, complex magnon band topology
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Möbius molecules and fragile Mott insulators

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• Mott insulators with boundary zeros
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• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• Electronic properties, correlated topology and Green's function zeros
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Interaction-induced crystalline topology of excitons
• Altermagnetic Instabilities from Quantum Geometry
• Exciton Berryology
• Many-Body Quantum Geometric Dipole
• The destiny of obstructed atomic insulator under correlation
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Quantum Restored Symmetry Protected Topological Phases
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene