arXiv Open Access 2006

On the Degenerate Multiplicity of the $sl_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity

Tetsuo Deguchi

Lihat Sumber

Abstrak

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 $sl_2$ loop algebra symmetry if the $q$ parameter is given by a root of unity, $q_0^{2N}=1$, 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 ${\bar d}_k^{\pm}$, which leads to evaluation parameters $a_j$. If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.

Topik & Kata Kunci

cond-mat.stat-mech math-ph nlin.SI

Penulis (1)

Tetsuo Deguchi

Format Sitasi

APA MLA BibTeX

Deguchi, T. (2006). On the Degenerate Multiplicity of the $sl_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity. https://arxiv.org/abs/cond-mat/0602427

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2006
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓