Droplet states in quantum XXZ spin systems on general graphs

Abstract

We study XXZ spin systems on general graphs. In particular, we describe the formation of droplet states near the bottom of the spectrum in the Ising phase of the model, where the Z-term dominates the XX-term. As key tools we use particle number conservation of XXZ systems and symmetric products of graphs with their associated adjacency matrices and Laplacians. Of particular interest to us are strips and multi-dimensional Euclidean lattices, for which we discuss the existence of spectral gaps above the droplet regime. We also prove a Combes-Thomas bound which shows that the eigenstates in the droplet regime are exponentially small perturbations of strict (classical) droplets.

32 pages, 5 figures, updated version with additional graph-theoretic references

References in corpus (3)

• Low-energy Fock-space localization for attractive hard-core particles in disorder
• Manifestations of dynamical localization in the disordered XXZ spin chain
• Bounds on the entanglement entropy of droplet states in the XXZ spin chain

Cited by in corpus (8)

• How much delocalisation is needed for an enhanced area law of the entanglement entropy?
• Hamiltonicity of Token Graphs of some Join Graphs
• Entanglement bounds in the XXZ quantum spin chain
• The automorphism groups of some token graphs
• Bounds on the bipartite entanglement entropy for oscillator systems with or without disorder
• Independence numbers of some double vertex graphs and pair graphs
• Entanglement Entropy Bounds in the Higher Spin XXZ Chain
• Hamiltonicity of the Double Vertex Graph and the Complete Double Vertex Graph of some Join Graphs