The Sachdev-Ye-Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density-density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density-density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.

Sachdev-Ye-Kitaev（SYK）模型是在分析上易于处理的强相互作用系统的罕见示例。可操作性的出现是因为该模型在设计上基本上是无结构的，因此是人工的：尽管交互作用仅限于两​​体项，但是交互作用矩阵元素是“随机的”，因此相应的交互作用算子不会与局部密度相对应。与常规的密度-密度类型的交互作用不同，从这个意义上说，SYK交互作用是不可积分的。我们在这里研究了（复杂）SYK模型的一种变体，它恢复了这种可集成性。它具有随机的单项术语和密度-密度-类型的交互作用。我们目前的数值研究表明，该模型展示出由几个中间相（包括一个混沌相）隔开的两个可整合相。混沌相带有几个特征性SYK特征，包括频谱统计和格林函数的频率定标，因此应绝热地连接到原始SYK模型的非费米液相。因此，我们的模型哈密顿量提供了从SYK模型到微观现实主义的桥梁。