Singular eigenstates in the even (odd) length Heisenberg spin chain
Singular eigenstates in the even (odd) length Heisenberg spin chain
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偶（奇）长海森堡自旋链中的奇异本征态
DOI：
10.1088/1751-8113/48/17/175207
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Pulak Ranjan Giri and Tetsuo Deguchi
中科院分区：
文献类型：
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作者：
Juan Feng;Lin Wang;and Wen Chen;Pulak Ranjan Giri and Tetsuo Deguchi
我们研究了正则化对某些特定下自旋扇区中偶(奇)长自旋-1/2XXX链奇异解的影响。特别地，得到了定长链中三个下自旋扇区的Bethe本征态的解析表达式及其数值形式。对于偶数长链，如果奇异解在其速度的符号变化下不变，则Bethe ansatz方程在偶(奇)下自旋扇区被化为(M-2)/2((M-3)/2)方程组.对于三个下自旋扇区中的奇N长链，解析地证明了在任意有限长的N=3\Left(2k+1\Right)形式的自旋链中存在奇解，其中k=1，2，3，\cdots。对于某些奇数长度的自旋-1/2XXX链，在四个向下自旋区域内不存在奇异解。
We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \{\lambda_\alpha\} are invariant under the sign changes of their rapidities {\lambda_\alpha\}=\{-\lambda_\alpha\} , then the Bethe ansatz equations are reduced to a system of (M-2)/2 ((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N= 3\left(2k+1\right) with k=1, 2, 3, \cdots. It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.