Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain
2005, v.11, Issue 2, 223-236
We consider the highly anisotropic ferromagnetic spin 1/2 Heisenberg chain with periodic boundary conditions. In each sector of constant total z component of the spin, we develop convergent expansions for the lowest band of eigenvalues and eigenfunctions. These eigenstates describe droplet states in which the spins essentially form a single linear droplet which can move. Our results also give a convergent expansion for the dispersion relation, i.e., the energy of the droplet as a function of its momentum. The methods used are from [N. Datta and T. Kennedy, Expansions for one quasiparticle states in spin 1/2 systems, J. Stat. Phys., 2002, v.108, 373-399, arXiv:cond-mat/0104199] and [N. Datta and T. Kennedy, Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature, Commun. Math. Phys., 2003, v.236, 477-511, arXiv:math-ph/0208026], and this short paper should serve as a pedagogic introduction to those papers.
Keywords: droplets,XXZ ferromagnet,quantum spin chain