The spectral gap of a fractional quantum Hall system on a thin torus

Abstract

We study a fractional quantum Hall system with maximal filling $\nu =1/3$ in the thin torus limit. The corresponding Hamiltonian is a truncated version of Haldane's pseudopotential, which upon a Jordan-Wigner transformation is equivalent to a one-dimensional quantum spin chain with periodic boundary conditions. Our main result is a lower bound on the spectral gap of this Hamiltonian, which is uniform in the system size and total particle number. The gap is also uniform with respect to small values of the coupling constant in the model. The proof adapts the strategy of individually estimating the gap in invariant subspaces used for the bosonic $\nu =1/2$ model to the present fermionic case.

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• Dynamical abelian anyons with bound states and scattering states
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
• On a bulk gap strategy for quantum lattice models