论文标题
无序的Haldane-Shastry模型
Disordered Haldane-Shastry model
论文作者
论文摘要
Haldane-Shastry模型是研究最多的相互作用自旋系统之一。 Yangian对称性使其完全可以解决，并且该模型具有半离子的激发。我们通过允许旋转位于单位圆上的随机位置并研究特征态的特性来将障碍引入Haldane-Shastry模型。在弱障碍下，频谱类似于清洁的霍尔丹省模型的光谱。在强大的障碍下，模型中的远距离相互作用并不是一个简单的力量定律。频谱中间的本征态遵循体积定律，但系数较小，因此熵远小于对厄贡系统。此外，能级间距统计量既不是泊松人，也不是wigner-dyson型。因此，在有力障碍的强度行为是非多体性局部化类型的非菌相的一个例子，在具有远距离相互作用和SU（2）对称性的模型中。
The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the Haldane-Shastry model by allowing the spins to sit at random positions on the unit circle and study the properties of the eigenstates. At weak disorder, the spectrum is similar to the spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range interactions in the model do not decay as a simple power law. The eigenstates in the middle of the spectrum follow a volume law, but the coefficient is small, and the entropy is hence much less than for an ergodic system. In addition, the energy level spacing statistics is neither Poissonian nor of the Wigner-Dyson type. The behavior at strong disorder hence serves as an example of a non-ergodic phase, which is not of the many-body localized kind, in a model with long-range interactions and SU(2) symmetry.
