Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity

详细信息    查看全文

• 作者：Azat M. Gainutdinov^a ; ^b ; ^{azat.gainutdinov@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author} ; Rafael I. Nepomechie^c ; ^{nepomechie@physics.miami.edu" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：909
• 期：Complete
• 页码：796-839
• 全文大小：633 K

文摘

For generic values of q  , all the eigenvectors of the transfer matrix of the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0550321316301493&_mathId=si1.gif&_user=111111111&_pii=S0550321316301493&_rdoc=1&_issn=05503213&md5=a63689b0d681fadb9223843d3e79daa3" title="Click to view the MathML source">U_qsl(2)class="mathContainer hidden">class="mathCode">$U_{q}sl(2)$-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q   is a root of unity (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0550321316301493&_mathId=si2.gif&_user=111111111&_pii=S0550321316301493&_rdoc=1&_issn=05503213&md5=4d74575fa6dda6f2712430a5f106a1d2" title="Click to view the MathML source">q=e^iπ/pclass="mathContainer hidden">class="mathCode">$q=e^{i\pi /p}$ with integer class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0550321316301493&_mathId=si3.gif&_user=111111111&_pii=S0550321316301493&_rdoc=1&_issn=05503213&md5=189624bbdca1c33eb26fa47aaa2cc649" title="Click to view the MathML source">p≥2class="mathContainer hidden">class="mathCode">$p\ge 2$), the Bethe equations acquire continuous solutions, and the transfer matrix develops Jordan cells. Hence, there appear eigenvectors of two new types: eigenvectors corresponding to continuous solutions (exact complete p-strings), and generalized eigenvectors. We propose general ABA constructions for these two new types of eigenvectors. We present many explicit examples, and we construct complete sets of (generalized) eigenvectors for various values of p and N.