Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-06-09
J.Phys.A29:1629-1638,1996
Physics
High Energy Physics
High Energy Physics - Theory
Revtex file with 2 figures. Complementary remarks added
Scientific paper
10.1088/0305-4470/29/8/011
We study boundary bound states using the Bethe ansatz formalism for the finite $XXZ$ $(\Delta>1)$ chain in a boundary magnetic field $h$. Boundary bound states are represented by the ``boundary strings'' similar to those described in the work of H.Saleur, S.Skorik. We find that for certain values of $h$ the ground state wave function contains boundary strings, and from this infer the existence of two ``critical'' fields in agreement with the results of Jimbo et al. An expression for the vacuum surface energy in the thermodynamic limit is derived and found to be an analytic function of $h$. We argue that boundary excitations appear only in pairs with ``bulk'' excitations or with boundary excitations at the other end of the chain. We mainly discuss the case where the magnetic fields at the left and the right boundaries are antiparallel, but we also comment on the case of the parallel fields. In the Ising ($\Delta=\infty$) and isotropic ($\Delta=1$) limits our results agree with those previously known.
Kapustin A. A.
Skorik Sergei
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