Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

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.

72 pages, 25 figures and lots of references. Comments are welcome; (v2) Added references

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• Strange metals as ersatz Fermi liquids
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• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Sum Rules and Ward Identities in the Kondo Lattice
• Symmetry Breaking in Coupled SYK or Tensor Models
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
• Charge transport in the Hubbard model at high temperatures: triangular versus square lattice
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• Shining light on transition metal oxides: unveiling the hidden Fermi Liquid
• On systems of maximal quantum chaos
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• Spin-boson coupling in continuous-time quantum Monte Carlo
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• Zero-Temperature Magnetic Transition in an Easy-Axis Kondo Lattice Model
• Dirac Fast Scramblers
• Heavy non-degenerate electrons in doped strontium titanate
• Magnetic quantum phase transition in an anisotropic Kondo lattice
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• Low temperature $T$-linear resistivity due to umklapp scattering from a critical mode
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• Gravitational dual of averaged free CFT's over the Narain lattice
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• Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
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• Planckian Metal at a Doping-Induced Quantum Critical Point
• Bekenstein-Hod Universal Bound on Information Emission Rate Is Obeyed by LIGO-Virgo Binary Black Hole Remnants
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• Quantum phase transition at non-zero doping in a random $t$-$J$ model
• Tunneling through an Eternal Traversable Wormhole
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• Critical metallic phase in the overdoped random $t$-$J$ model
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• Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
• Metal-insulator transition in a random Hubbard model
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• NaxCoO2: Enhanced low-energy excitations of electrons on a 2D triangular lattice
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• Thermalization in different phases of charged SYK model
• Anomalous density fluctuations in a random $t$-$J$ model
• Many-body energy invariant for $T$-linear resistivity
• ω/T scaling of the optical conductivity in strongly correlated layered cobalt oxide
• On Planckian limit for inelastic relaxation in metals
• Pairing by a dynamical interaction in a metal

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• Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two dimensional Hubbard model
• Engineering random spin models with atoms in a high-finesse cavity
• Dynamical quantum phase transitions in SYK Lindbladians
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals
• Binary-coupling sparse SYK: an improved model of quantum chaos and holography
• Spin-liquid insulators can be Landau's Fermi liquids
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• A fast time domain solver for the equilibrium Dyson equation
• Engineering SYK interactions in disordered graphene flakes under realistic experimental conditions
• Quantum bounds on the generalized Lyapunov exponents
• Disorder-dominated quantum criticality in moiré bilayers
• Can neural quantum states learn volume-law ground states?
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Critical metallic phase in the overdoped random $t$-$J$ model
• Quantum chaos and phase transition in the Yukawa-SYK model
• Quantum oscillations in a doped Mott insulator beyond Onsager's relation
• Superconductor--Insulator Transition in a non-Fermi Liquid
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Zero sound and higher-form symmetries in compressible holographic phases
• A Criterion for Strange Metallicity in the Lorenz Ratio
• Collective density fluctuations of strange metals with critical Fermi surfaces
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Jamming and Unusual Charge Density Fluctuations of Strange Metals
• Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models
• Optical spin conductivity in ultracold quantum gases
• Superfluidity from correlations in driven boson systems
• Incoherent transport in a model for the strange metal phase: Memory-matrix formalism
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in strong correlation limit
• Notes on Quantum oscillation for Hatsugai-Kohmoto model
• Symmetry classification of typical quantum entanglement
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model
• $T-$linear resistivity from magneto-elastic scattering: application to PdCrO${}_2$
• Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
• Tunable phase transition in a dissipative two-spin system: A renormalization group study
• Quantum-critical transport in marginal Fermi liquids
• Mott domain walls: a (strongly) non-Fermi liquid state of matter