We discuss the bulk gap for a truncated 1/3-filled Haldane pseudopotential for the fractional quantum Hall effect in the cylinder geometry. In the case of open boundary conditions, a lower bound on the spectral gap (which is uniform in the volume and particle number) accurately reflects the presence of edge states, which do not persist into the bulk. A uniform lower bound for the Hamiltonian with periodic boundary conditions is also obtained. Both of these bounds are proved by identifying invariant subspaces to which spectral gap and ground state energy estimating methods originally developed for quantum spin Hamiltonians are applied. Customizing the gap technique to the invariant subspace, however, we are able to avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions. The same approach can also be applied to prove a bulk gap for the analogously truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. This is based off joint work with S. Warzel.

A bulk gap in the presence of edge states for a truncated Haldane pseudopotential Sponsored by the Meyer Fund