发表机构
Humboldt-Universität zu Berlin; Laboratoire de Physique de l’ENS, Sorbonne Université（柏林洪堡大学; 巴黎高等师范学校物理实验室，索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究福井-川上（FK）链的谱与隐藏对称性，发现其反周期边界条件下对应最小极化长程模型，具有隐藏的$\frak{gl}(1|1)$对称性，可关联HS基元与超对称对应物。
AI 中文摘要
福井和川上证明，三角型Haldane–Shastry（HS）自旋链可通过引入扭曲边界条件发生形变。本研究重新考察由此得到的扭曲HS链，将其命名为福井-川上（FK）链。我们利用其与（未扭曲）HS链的直接关联，分析FK链的谱随扭曲参数的变化关系，这使得我们能够解释为何部分谱可由福井和川上的扭曲Bethe方程描述，且可通过Yangian最高权态构建。这些态与HS链类似，可被称为“基元（motifs）”的组合数据标记，涵盖部分（形变后的）后代态。我们进一步证明，存在其他不遵循这些Bethe方程的后代态，其能量可表示为两个单粒子能量之和，暗示存在额外的隐藏对称性。随后我们聚焦于反周期边界条件这一特殊情况，证明该链与Basu-Mallick、Finkel和González-López近期提出的“最小极化”长程模型完全一致。值得注意的是，这一关联表明反周期链具有隐藏的$\boldsymbol{\frak{gl}(1|1)}$对称性，我们利用该对称性将HS基元与其“超对称”$\boldsymbol{\frak{gl}(1|1)}$对应物关联起来。
英文摘要
Fukui and Kawakami showed that the trigonometric Haldane--Shastry (HS) spin chain can be deformed by introducing twisted boundary conditions. In this work we revisit the resulting twisted HS chains, which we call Fukui--Kawakami (FK) chains. We analyse their spectra in dependence of the twist parameter, utilising a direct connection with the (untwisted) HS chain. This allows us to explain why part of the spectrum can be described by Fukui and Kawakami's twisted Bethe equations, and can be constructed from Yangian highest weight states. These states can be labelled by combinatorial data called `motifs', as in the HS chain, which cover some of the (deformed) descendants. We furthermore show that there are other descendants which do not follow from these Bethe equations, but whose energy can be described as a sum of two single-particle energies, suggesting additional hidden symmetries. We then focus on the special case of antiperiodic boundary conditions, and show that this chain coincides with the `minimally polarised' long-range model recently introduced by Basu-Mallick, Finkel, and González-López. Remarkably, this connection implies that the antiperiodic chain has a hidden $\mathfrak{gl}(1|1)$-symmetry, which we use to relate the HS motifs to their `supersymmetric' $\mathfrak{gl}(1|1)$ counterparts.
Comments16 pages, 4 figures
