Simplified topological invariants for interacting insulators

Abstract

We propose general topological order parameters for interacting insulators in terms of the Green's function at zero frequency. They provide an unified description of various interacting topological insulators including the quantum anomalous Hall insulators and the time reversal invariant insulators in four, three and two dimensions. Since only Green's function at zero frequency is used, these topological order parameters can be evaluated efficiently by most numerical and analytical algorithms for strongly interacting systems.

Published version

References in corpus (8)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Topological Mott Insulators
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Exciton condensation and charge fractionalization in a topological insulator film

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• Correlation effects in two-dimensional topological insulators
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• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Phonon-induced topological transitions and crossovers in Dirac materials
• Characterization of a topological Mott insulator in one dimension
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Phonon-induced topological insulation
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Heavy Weyl fermion state in CeRu${}_4$Sn${}_6$
• Pseudospin 3/2 Fermions, Type-II Weyl Semimetals and Critical Weyl Semimetals in Tricolor Cubic Lattice
• End states in a 1-D topological Kondo insulator
• Tracing the nonequilibrium topological state of Chern insulators
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Change of an insulator's topological properties by a Hubbard interaction
• Topological properties of the bond-modulated honeycomb lattice
• Topological phase in a two-dimensional metallic heavy-fermion system
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Short-ranged interaction effects on $Z_2$ topological phase transitions
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Spontaneous loop-spin current with topological characters in the Hubbard model