Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus

Abstract

We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interaction and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula, and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

9 pages

References in corpus (30)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant 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
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Correlated Topological Insulators with Mixed Valence
• Exciton condensation and charge fractionalization in a topological insulator film
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Fractional topological insulators in three dimensions
• Hybridization, Inter-Ion Correlation, and Surface States in the Kondo Insulator SmB6
• Theory of orbital magnetoelectric response
• Topological invariants and interacting one-dimensional fermionic systems
• Topological field theory and thermal responses of interacting topological superconductors
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Plutonium hexaboride is a correlated topological insulator
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Z2 topological invariants in two dimensions from quantum Monte Carlo
• Interaction induced topological phase transition in Bernevig-Hughes-Zhang model
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Change of an insulator's topological properties by a Hubbard interaction
• Topological phase in a two-dimensional metallic heavy-fermion system

Cited by in corpus (20)

• Classification of topological quantum matter with symmetries
• Interacting topological insulators: a review
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Collective modes in nodal line semimetals
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Topological nodal line semimetals in holography
• Geometric orbital magnetization in adiabatic processes
• Topological invariants for holographic semimetals
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• From Trivial Kondo Insulator Ce${}_3$Pt${}_3$Bi${}_4$ to Topological Nodal-line Semimetal Ce${}_3$Pd${}_3$Bi${}_4$
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Topological and conventional phases of a three dimensional electron glass
• Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations
• Topological Solitons in Su-Schrieffer-Heeger Chain with periodic hopping modulation, domain walls and disorder
• Stability of Topological character of Weyl Semi-metal, and Topological Dipole in Holography
• Topological bosonic states on ribbons of honeycomb lattice
• Fate of gapless edge states in two-dimensional topological insulators with Hatsugai-Kohmoto interaction
• Quantum magnetism of topologically-designed graphene nanoribbons
• Topological invariant for holographic Weyl-${\mathrm{Z}}_2$ semimetal
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction