A Schr\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs
Abstract
We consider the spin-J XXZ-Hamiltonian on general graphs G and show its equivalence to a direct sum of discrete many-particle Schr\"odinger type operators on what we call "N-particle graphs with maximal local occupation number M", where the kinetic term is described by a weighted Laplacian. Generalizing previous results for the spin-1/2 case, we give sufficient conditions for the existence of spectral gaps above the low-lying droplet band when the underlying graph G is (i) the chain and (ii) a strip of width L.
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