On the Degenerate Multiplicity of the sl2 Loop Algebra for the 6V Transfer Matrix at Roots of Unity
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چکیده
We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl2 loop algebra symmetry if the q parameter is given by a root of unity, q 0 = 1, for an integer N . We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regular Bethe ansatz eigenvector in the sectors is a highest weight vector and derive the highest weight d̄k , which leads to evaluation parameters aj . If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.
منابع مشابه
The sl2 loop algebra symmetry of the twisted transfer matrix of the six vertex model at roots of unity
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تاریخ انتشار 2006