Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-28
Nucl.Phys.B430:615-632,1994
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file with LaTeX figures, 24 pages, 1 PiCTeX figure
Scientific paper
10.1016/0550-3213(94)90162-7
The $sl_q(2)$-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for $q$ equal to a root of unity possess a finite number of ``good'' representations with non-zero q-dimension and ``bad'' ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into ``good'' and ``bad'' states. A ``good'' state may be described by a path of only ``good'' representations. It is shown that the ``good'' states are given by all ``good'' Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive parity strings (in the language of Takahashi) are allowed. Applying Bethe's string counting technique completeness of the ``good'' Bethe states is proven, i.e. the same number of states is found as the number of all restricted path's on the $sl_q(2)$-Bratteli diagram. It is the first time that a ``completeness" proof for an anisotropic quantum invariant reduced Heisenberg model is performed.
Juettner G.
Karowski Michael
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