论文标题
可集成的（超级）折衷的自旋链
The Integrable (Hyper)eclectic Spin Chain
论文作者
论文摘要
我们通过包括最大数量的变形参数来完善最近引入的折衷自旋链的概念。这些模型是可集成的，最近的N-State旋转链，具有非常简单的非温和汉密尔顿人。事实证明，它们在多片扇区（n> 2）中是不可用的，其中它们的“光谱”由复杂的任意大小和多重性的约旦块集合。我们展示了量子反向散射方法的方式和原因，试图普遍适用于可集成的最近邻居旋转链，本质上无法再现此频谱的细节。然后，对于n = 3，我们通过多种分析和数值技术提供详细的证据，表明频谱不是“随机”，而是显示出令人惊讶的微妙和规则模式，这些模式此外还表现出通用性，这些模式在通用变形参数上表现出普遍性。我们还引入了一个新的模型，即高分子自旋链，除一个参数外，所有参数均为零。尽管其哈密顿量极为简单，但它似乎仍然将上述“通用”光谱重现为更复杂的总体光谱的子集。我们的模型灵感来自n = 4个超级阳米尔斯理论的强扭曲，双刻度变形的一环扩张算子的一部分。
We refine the recently introduced notion of eclectic spin chains by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n>2), where their "spectrum" consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not "random", but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above "generic" spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of N=4 Super Yang-Mills Theory.
