This is a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. The phase diagrams of a number of models of such a local electronic correlation are explored, employing a dynamical mean-field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions that display SYK physics. The models studied include the single-band Hubbard model, the $t\text{−}J$ model, and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. Also examined are non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multiorbital atom, with the SYK atoms arranged in an infinite lattice. Connections are made to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large-$N$ theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, an overview of the links between the SYK model and quantum gravity is presented, and the review ends with an outlook on open questions.

中文翻译：

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Sachdev-Ye-Kitaev 模型及其他模型：非费米液体的窗口

本文回顾了无准粒子激发的可压缩量子多体系统的 Sachdev-Ye-Kitaev (SYK) 模型，及其与凝聚态物理中非费米液体的各种理论研究的联系。该评论是在对相关电子材料进行大量实验观察的背景下进行的。金属中的强相关性通常与它们接近由电子之间的局部库仑斥力产生的到绝缘体的莫特跃迁有关。在存在随机自旋交换相互作用的情况下，采用动态平均场理论，探索了这种局域电子关联的许多模型的相图。数值分析和解析解，使用重正化群方法和大自旋简并展开，得出显示 SYK 物理的关键区域。研究的模型包括单带哈伯德模型、$t\text{-}J$模型，以及存在随机自旋交换相互作用的两带近藤-海森堡模型。还检查了通过将具有随机四费米子相互作用的每个 SYK 模型视为多轨道原子而获得的非费米液体，其中 SYK 原子排列在无限晶格中。通过将费米液体与无间隙玻色子耦合获得，在没有空间无序的情况下，与没有任何低能准粒子的尖锐费米表面理论建立了联系；一个系统化的大$氮$这种具有 SYK 特性的临界费米面理论是通过对具有随机玻色子-费米子耦合的理论集合进行平均而获得的。最后，概述了 SYK 模型和量子引力之间的联系，并以对悬而未决的问题的展望结束了评论。