论文标题
从费米子自旋 - 卡洛格罗 - 距离模型到冻结
From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
论文作者
论文摘要
Haldane-Shastry自旋链具有无数的显着特性，包括扬式对称性，对于自旋$ 1/2 $，明确的最高权重量特征向量具有（案例$ $α= 1/2 $）jack polynomials。这源于自旋 - 卡洛格 - 泽兰模型，该模型在特殊的“冷冻”极限下还原为Haldane-Shastry。 在这项工作中，我们澄清了各种观点，据我们所知，文献中缺少。我们有两个主要结果。首先，我们表明，冻结$ \ mathit {fermionic} $ spin-1/2 calogero-Sutherland模型自然地说明了Haldane-Shastry Wave函数的精确形式，包括Vandermonde因子平方。其次，我们使用费米金框架来证明伯纳德·戈丁·哈尔达内 - 帕斯奎尔（Bernard-Gaudin-Haldane-Pasquier）的主张是$ su（r）$ - 版本的yangian最高权威特征值 - haldane-shastry链的版本是由freezing $ su（r-1）$ spin-calogero-sut-calogero-sutherland eigenvectors在$ $ su（$ su）中产生的。
The Haldane-Shastry spin chain has a myriad of remarkable properties, including Yangian symmetry and, for spin $1/2$, explicit highest-weight eigenvectors featuring (the case $α= 1/2$ of) Jack polynomials. This stems from the spin-Calogero-Sutherland model, which reduces to Haldane-Shastry in a special `freezing' limit. In this work we clarify various points that, to the best of our knowledge, were missing in the literature. We have two main results. First, we show that freezing the $\mathit{fermionic}$ spin-1/2 Calogero-Sutherland model naturally accounts for the precise form of the Haldane-Shastry wave functions, including the Vandermonde factor squared. Second, we use the fermionic framework to prove the claim of Bernard-Gaudin-Haldane-Pasquier that the Yangian highest-weight eigenvectors of the $SU(r)$-version of the Haldane-Shastry chain arise by freezing $SU(r-1)$ spin-Calogero-Sutherland eigenvectors at $α= 1/2$.
