A Schrödinger Operator Approach to Higher Spin XXZ Systems on General Graphs

Abstract

We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schrödinger 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 $\mathcal{G}$ is (i) the chain and (ii) a strip of width $L$.

arXiv comment16 pages, Contribution to the Proceedings of the Arizona School of Analysis and Mathematical Physics 2018, corrected a few typos