Pierluigi Contucci, Bruno Nachtergaele, Wolfgang Spitzer
The Ferromagnetic Heisenberg XXZ chain in a pinning field
(411K, Latex, 8 eps figures)
ABSTRACT. We investigate the effect of a magnetic field supported at a
single lattice site on the low-energy spectrum of the
ferromagnetic Heisenberg XXZ chain. Such fields, caused by
impurities, can modify the low-energy spectrum significantly by
pinning certain excitations, such as kink and droplet states. We
distinguish between different boundary conditions (or sectors),
the direction and also the strength of the magnetic field. E.g.,
with a magnetic field in the z-direction applied at the origin
and ++ boundary conditions, there is a critical field strength
B_c (which depends on the anisotropy of the Hamiltonian and the
spin value) with the following properties: for B < B_c there is a
unique ground state with a gap, at the critical value, B_c,
there are infinitely many (droplet) ground states with gapless
excitations, and for B > B_c there is again a unique ground state
but now belonging to the continuous spectrum. In contrast, any
magnetic field with a non-vanishing component in the xy-plane
yields a unique ground state, which, depending on the boundary
conditions, is either an (anti)kink, or an (anti)droplet state.
For such fields, i.e., not aligned with the z-axis, excitations
always have a gap and we obtain a rigorous lower bound for that
gap.