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Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
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abstract
We present 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. We explore the phase diagrams of a number of models of such local electronic correlation, 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 which display SYK physics. The models studied include the single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect 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, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.
Forward citations
Cited by 7 Pith papers
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Linear Resistivity from Spatially Random Interactions and the Uniqueness of Yukawa Coupling
Only the two-dimensional spatially random Yukawa coupling, among all (ψ†ψ)^n φ^m scalar couplings, yields linear-in-temperature resistivity in the large-N SYK-rised framework.
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Hall Angle of a Spatially Random Vector Model
In a spatially random vector-coupling model with a magnetic field, linear-T resistivity persists while the Hall angle follows normal 1/T behavior rather than the strange-metal T^2 law.
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Theory of Strongly Correlated Systems: An Introduction to Sachdev-Ye-Kitaev Model
A self-contained review deriving the SYK model's large-N, large-q, Schwarzian, and Keldysh results, including linear-in-T resistivity and mean-field criticality in the complex SYK model.
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The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
The paper attributes the cuprate 'foot' to a disordered spin-density-wave transition and the 'fan' to a disorder-tuned FL-to-FL* Fermi-volume-changing transition described by a two-dimensional Yukawa-SYK model.
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