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 (70)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• 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 insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological quantum chemistry
• Topological superconductors: a review
• The (High Quality) Topological Materials In The World
• Mott physics and band topology in materials with strong spin-orbit interaction
• Zoo of quantum-topological phases of matter
• Frequency-dependent local interactions and low-energy effective models from electronic structure calculations
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological classification of crystalline insulators through band structure combinatorics
• Symmetry Protected Topological phases of Quantum Matter
• 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
• Fragile Topology and Wannier Obstructions
• Interacting topological insulators: a review
• Single particle Green's functions and interacting topological insulators
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Detection of Symmetry Protected Topological Phases in 1D
• Is 1T-TaS${}_2$ a 40 year old quantum spin liquid?
• Classification of Topological Insulators and Superconductors
• 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
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Gauging spatial symmetries and the classification of topological crystalline phases
• 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
• Band Representations and Topological Quantum Chemistry
• Probing Electron Correlation via Attosecond XUV Pulses in the Two-Photon Double Ionization of Helium
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Topological states from topological crystals
• Topological Hamiltonian as an Exact Tool for Topological Invariants
• Orbital-driven Mottness collapse in 1T-TaS2-xSex transition metal dichalcogenide
• Topological invariants for interacting topological insulators with inversion symmetry
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Symmetry indicators of band topology
• Generalized two-leg Hubbard ladder at half-filling: Phase diagram and quantum criticalities
• Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
• Real-space recipes for general topological crystalline states
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite
• Charge and Spin Structures of a $d_{x^2-y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator
• Fragile Mott Insulators
• Electronic Mechanism of Superconductivity in the Cuprates, C${}_{60}$, and Polyacenes
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Local Antiferromagnetic Correlations and $d_{x^2-y^2}$ Pairing
• 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
• Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model
• Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model
• Möbius molecules and fragile Mott insulators

Cited by in corpus (15)

• Mott insulators with boundary zeros
• Failure of Topological Invariants in Strongly Correlated Matter
• 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