Bruno Nachtergaele, Shannon Starr
Droplet States in the XXZ Heisenberg Chain
(255K, LaTeX with 2 eps figures)
ABSTRACT. We consider the ground states of the ferromagnetic XXZ chain with
spin up boundary conditions in sectors with a fixed number of down
spins. This forces the existence of a droplet of down spins in the
system. We find the exact energy and the states that describe these
droplets in the limit of an infinite number of down spins. We also
prove that the droplet states, which were known to be separated by
an energy gap from the ground state, are also separated by an energy
gap from the remainder of the spectrum, i.e., they form an isolated
band. We also prove the analogous results for finite chains with
periodic boundary conditions and for the infinite chain.