Quantization of Hall Conductance for Interacting Electrons on a Torus

Abstract

We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e 2 /h, up to exponentially small corrections in the linear size L. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.

Universality of the Hall Conductivity in Interacting Electron Systems

“…, P n , we can enclose the points x(f ) belonging to the set P j in a box: in this way, assuming that all the points x(f ), f ∈ ∪ i P i , are distinct, we obtain n disjoint boxes. Given these definitions, if 38) where:…”

Non-Hermitian fractional quantum Hall states

“…In Fig. 2(d), we have numerically observed that the Berry curvature is almost independent of θ's, which implies that the computation of the Chern number may be simplified by defining the non-Hermitian counterpart of the one-plaquet Chern number for the Hermitian case [76][77][78][79]. We leave the extension of oneplaquet Chern number to non-Hermitian systems as a future work.…”

On ℤ2-indices for ground states of fermionic chains

“…Newer methods for higher-dimensional spin systems are also in development [25]. There has also been several results concerning stability of topological invariants such as the Hall conductance in interacting fermion systems [7,8,9,33,37,47].…”