论文标题
一类新颖的翻译不变的旋转链，具有远距离相互作用
A novel class of translationally invariant spin chains with long-range interactions
论文作者
论文摘要
我们介绍了一类新的开放，翻译不变的自旋链，并取决于自旋置换和（极化）自旋逆转操作员，其中包括Haldane-Shastry链，作为特定的变性情况。新班级的特点是，哈密顿量在“扭曲”翻译下不变，将普通的翻译与链条一端的旋转翻转相结合。它包括一个具有椭圆形自旋相互作用的非凡模型，在具有抗周期边界条件的XXX Heisenberg模型之间平滑插值，以及一个新的开放链，其位点在半圆形上均匀间隔，并且相互作用与旋转之间的距离的正方形成正比。我们能够以封闭形式计算后一个链的分区功能，从而通过一对独立的su（1 | 1）和$ {\ rm su}（m/2）$ MOTIFS获得完整的频谱描述。这意味着，在Yangians $ y $（gl（1 | 1））和$ y $（gl $（0 | m/2）$）的直接总和下，甚至$ m $型号是不变的。我们还分析了新链谱的几个统计特性。特别是，我们表明它是高度退化的，这强烈表明存在着基础（扭曲的）Yangian对称性，这也是奇数$ m $的。
We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under "twisted" translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and ${\rm su}(m/2)$ motifs when the number $m$ of internal degrees of freedom is even. This implies that the even $m$ model is invariant under the direct sum of the Yangians $Y$(gl(1|1)) and $Y$(gl$(0|m/2)$). We also analyze several statistical properties of the new chain's spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd $m$.
