Insulator, conductor and commensurability: a topological approach

Abstract

I discuss a topological relation of the conduction property of a many-particle system on a periodic lattice at zero temperature to the energy spectrum. When the particle number per unit cell is an irreducible fraction $p/q$, an insulator must have $q$ low-lying states of energy $o(1/L)$ in one dimension and of energy $o(1)$ in two dimensions, where $L$ is the linear system size.

4 pages (no figures) in REVTEX; revised version with minor corrections

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• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
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• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Laser-induced magnetization curve
• Topological degeneracy of non-Abelian states for dummies
• Insensitivity of bulk properties to the twisted boundary condition
• Non-local order parameters for the 1D Hubbard model
• The particle number in Galilean holography
• Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities
• Generalized $f$-Sum Rules and Kohn formulas on Non-linear Conductivities
• Geometric phases and the magnetization process in quantum antiferromagnets
• Quantum phase transitions from analysis of the polarization amplitude
• Heisenberg antiferromagnet on the Husimi lattice
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Flux quench in a system of interacting spinless fermions in one dimension
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Magnetic Phase Diagram of Frustrated Spin Ladder
• Metastable and localized Ising magnetism in $\alpha$-CoV${}_2$O${}_6$ magnetization plateaus
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases
• Bloch oscillations in the spin-1/2 XXZ chain
• Controlling inversion and time-reversal symmetries by subcycle pulses in the one-dimensional extended Hubbard model
• Drude weights in one-dimensional systems with a single defect
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension