A Schr\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs

Christoph Fischbacher

A Schr\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs

Mathematical Physics 2019-02-12 v2 math.MP

Authors: Christoph Fischbacher

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 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 $\mathcal{G}$ is (i) the chain and (ii) a strip of width $L$ .

Keywords

spin-j xxz model schrödinger operator general graphs spectral gaps discrete laplacian many-particle systems

Cite

@article{arxiv.1811.09899,
  title  = {A Schr\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs},
  author = {Christoph Fischbacher},
  journal= {arXiv preprint arXiv:1811.09899},
  year   = {2019}
}

Comments

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

A Schr\"odinger Operator Approach to Higher Spin XXZ Systems on General Graphs

Abstract

Keywords

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