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arXiv 2005.06030math-phcond-mat.stat-mechhep-thmath.MP
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Bethe能的解析延拓及其对$SL(2,\mathbb{C})$非紧自旋链热力学极限的应用

Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains

Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur

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50 pages
发表信息：
JHEP article number 69 (2020)
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摘要：

我们考虑的问题，解析连续的能量计算与Bethe的anasterian，所提出的非紧可积自旋链的研究。通过在Bethe方程中引入一个假想的广泛的扭曲，我们表明，人们可以扩展的解析连续的能量在标度极限周围的另一个“伪真空”坐在一个负数的Bethe根，以同样的方式围绕通常的伪真空。我们证明了这种方法可以用来计算无限体积极限下$SL(2,\mathbb{C})$可积自旋链的某些态的能级，并作为原理证明，通过小尺寸下的外推结果恢复了[1]（对于自旋$s=0, \bar{s}=-1$）中以前得到的基态值.这些结果代表，据我们所知，第一次（部分）描述的频谱$SL(2,\mathbb{C})$非紧凑的自旋链的热力学极限。

英文摘要：

We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another 'pseudo-vacuum' sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the $SL(2,\mathbb{C})$ integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [1] (for the case of spins $s=0, \bar{s}=-1$) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of $SL(2,\mathbb{C})$ non-compact spin chains in the thermodynamic limit.

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