论文标题
Bethe能量的分析延续并应用于$ SL（2，\ Mathbb {C}）$非压缩旋转链的热力学极限
Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
论文作者
论文摘要
我们考虑了由Bethe Ansatz计算出的分析持续能量的问题，这是通过研究非紧凑型整合旋转链的研究所致。通过在伯特方程中引入一个假想的广泛扭曲，我们表明，人们可以在另一个“伪数量”围绕一个负数的伯特根源上扩展能量的分析性延续，就像伯特（Bethe）根部一样，就像通常的伪vacuum一样。我们表明，该方法可用于计算$ sl（2，\ mathbb {c}）$的某些状态的能量水平，可在无限 - 数量限制中进行集成旋转链，作为原理的证明，恢复了先前在[1]中获得的地面价值（对于spins $ s = 0，\ bar s = 0，\ bar {s} = -1 $ $ slim slim slim shill sill sill sill sill sill sill sill sill sill sill sill sill sill sill sill sill sallapolApaPOLAPOLAPOLAPOLAPOLAPOLAPOLAPAPOLAPAPOLAPERAPESS INSRASE。据我们所知，这些结果代表了$ sl（2，\ mathbb {c}）的第一个（部分）描述。
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.
