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Dalhousie-AARMS AAMP Seminar: Amanda Young (Technical University of Munich)
November 19, 2021 @ 4:00 pm - 5:00 pm
Title: A bulk gap in the presence of edge states for a Haldanepseudopotential Abstract: In this talk, we discuss a recent result on a bulk gap for a truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boundary conditions, we prove a spectral gap above the highly degenerate ground-state space which is uniform in the volume and particle number. Our proofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the case of open boundary conditions, the lower bound on the spectral gap accurately reflects the presence of edge states, which do not persist into the bulk. Customizing the gap technique to the invariant subspace, we 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 1/3-filled Haldane pseudopotential for the fractional quantum Hall effect. Based off joint work with S. Warzel.
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom. If you would like to attend, please email the organizers for connection details.