Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain

Details Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain Expansions for Droplet States in the Ferromagnetic XXZ Heisenberg Chain

2003-10-27

arxiv.org/abs/math-ph/0310059v1

Markov Processes and Related Fields 11 , 223 (2005)

Physics

Mathematical Physics

submitted to the proceedings of the workshop "Low-energy states in quantum many-body systems", 29 January 2003, Cergy-Pontoise

Scientific paper

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 math-ph/0208026 and cond-mat/0104199, and this short paper should serve as a pedagogic introduction to those papers.

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