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.

arXiv comment72 pages, 25 figures and lots of references. Comments are welcome; (v2) Added references

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• Heavy-electron quantum criticality and single-particle spectroscopy
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• Kondo Breakdown and Hybridization Fluctuations in the Kondo-Heisenberg Lattice
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• Towards a statistical theory of transport by strongly-interacting lattice fermions
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• Thermal diffusivity and chaos in metals without quasiparticles
• Metallicity and superconductivity in doped strontium titanate
• Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions
• Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity
• Critical local moment fluctuations in the Bose-Fermi Kondo model
• Strange metallicity in the doped Hubbard model
• Quantum butterfly effect in weakly interacting diffusive metals
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• Memory matrix theory of magnetotransport in strange metals
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• Locality, Quantum Fluctuations, and Scrambling
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Evidence for a Non-Fermi-Liquid Phase in Ge-Substituted YbRh2Si2
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• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
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• Periodic-orbit theory of universal level correlations in quantum chaos
• Accessing scrambling using matrix product operators
• Linear-in temperature resistivity from an isotropic Planckian scattering rate
• Non-Fermi liquid behavior and scaling of low frequency suppression in optical conductivity spectra of CaRuO${}_3$
• Quantum-critical phase out of frustrated magnetism in a strongly correlated metal
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
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• Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Free Energy from Replica Wormholes
• Quantum ergodicity in the SYK model
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• Mixed-valence insulators with neutral Fermi surfaces
• Magnetotransport in a model of a disordered strange metal
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
• Hidden magnetism at the pseudogap critical point of a high temperature superconductor
• Monte Carlo Studies of Quantum Critical Metals
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
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• The Quantum Spherical p-Spin-Glass Model
• Fermi surfaces and gauge-gravity duality
• Quantum Boltzmann equation of composite fermions interacting with a gauge field
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• Dispersive SYK model: band structure and quantum chaos
• Holographic non-Fermi liquid fixed points
• Heavy Carriers and Non-Drude Optical Conductivity in MnSi
• Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
• On the relation between the magnitude and exponent of OTOCs
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Charge diffusion and the butterfly effect in striped holographic matter
• DC resistivity at the onset of spin density wave order in two-dimensional metals
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• Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures
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• "Bad Metal" Conductivity of Hard Core Bosons
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• Revival dynamics in a traversable wormhole
• Conductivity spectrum of ultracold atoms in an optical lattice
• Optical lattice platform for the SYK model
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• Strange metals as ersatz Fermi liquids
• SYK non Fermi Liquid Correlations in Nanoscopic Quantum Transport
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• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Quantum-critical pairing with varying exponents
• Strange metal from local quantum chaos
• A model for continuous thermal Metal to Insulator Transition
• A controlled expansion for certain non-Fermi liquid metals
• Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective
• Hyperscaling violation at the Ising-nematic quantum critical point in two dimensional metals
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions
• Sum Rules and Ward Identities in the Kondo Lattice
• Quantum-Critical Fluctuations in 2D Metals: Strange Metals and Superconductivity in Antiferromagnets and in Cuprates
• Symmetry Breaking in Coupled SYK or Tensor Models
• Non-ergodic extended states in the SYK model
• Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
• Quantum Quenches and Thermalization in SYK models
• Crossover of Charge Fluctuations across the Strange Metal Phase Diagram
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Charge transport in the Hubbard model at high temperatures: triangular versus square lattice
• An orbital-selective spin liquid in a frustrated heavy fermion spinel LiV${}_2$O${}_4$
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
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• Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
• From operator statistics to wormholes
• Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy Fermion Metals
• Adding Flavor to the Narain Ensemble
• Quantum criticality of granular SYK matter
• $T$-linear resistivity in models with local self-energy
• Spin-boson coupling in continuous-time quantum Monte Carlo
• On the Planckian bound for heat diffusion in insulators
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Poor Man's Understanding of Kinks Originating from Strong Electronic Correlations
• A new class of SYK-like models with maximal chaos
• Deconfined criticality and ghost Fermi surfaces at the onset of antiferromagnetism in a metal
• Zero-Temperature Magnetic Transition in an Easy-Axis Kondo Lattice Model
• Intrinsic superconducting instabilities of a solvable model for an incoherent metal
• The Mott-Ioffe-Regel limit and resistivity crossover in a tractable electron-phonon model
• Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model
• Magnetic quantum phase transition in an anisotropic Kondo lattice
• Heavy non-degenerate electrons in doped strontium titanate
• Dirac Fast Scramblers
• Non-quasiparticle transport and resistivity saturation: A view from the large-N limit
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• Low temperature $T$-linear resistivity due to umklapp scattering from a critical mode
• Thermalization and Possible Signatures of Quantum Chaos in Complex Crystalline Materials
• Out of equilibrium dynamics of a Quantum Heisenberg Spin Glass
• Compressible quantum phases from conformal field theories in 2+1 dimensions
• Gravitational dual of averaged free CFT's over the Narain lattice
• Static hole in a critical antiferromagnet: field-theoretic renormalization group
• Quantum-critical scale invariance in a transition metal alloy
• Constructing the AdS dual of a Fermi liquid: AdS Black holes with Dirac hair
• The infinite-range quantum random Heisenberg magnet
• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
• Semiclassical Analysis of Extended Dynamical Mean Field Equations
• Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode
• Thickening and sickening the SYK model
• Scaling properties of the optical conductivity of Bi-based cuprates
• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• Thermalization and chaos in QED${}_3$
• Planckian Metal at a Doping-Induced Quantum Critical Point
• A candidate Theory for the "Strange Metal" phase at Finite Energy Window
• Quantum tunneling dynamics in a complex-valued Sachdev-Ye-Kitaev model quench-coupled to a cool bath
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Bekenstein-Hod Universal Bound on Information Emission Rate Is Obeyed by LIGO-Virgo Binary Black Hole Remnants
• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Quantum Critical Point in the Spin Glass-Kondo Transition in Heavy Fermion Systems
• Tunneling through an Eternal Traversable Wormhole
• Quantum phase transition at non-zero doping in a random $t$-$J$ model
• Strange Half Metals and Mott Insulators in SYK Models
• The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids
• Deconfined metallic quantum criticality: A $U(2)$ gauge-theoretic approach
• Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
• Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models
• Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual
• Superconductivity from Luttinger surfaces: Emergent $\infty$-body SYK physics
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Out-of-time-ordered correlators of the Hubbard model: SYK strange metal in the spin freezing crossover region
• Gravitational collapse in SYK models and Choptuik-like phenomenon
• Critical metallic phase in the overdoped random $t$-$J$ model
• Rescuing a black hole in the large-$q$ coupled SYK model
• Dynamical scaling of charge and spin responses at a Kondo destruction quantum critical point
• Page Curve from Non-Markovianity
• Planckian relaxation delusion in metals
• Equivalence of single-particle and transport lifetimes from hybridization fluctuations
• NaxCoO2: Enhanced low-energy excitations of electrons on a 2D triangular lattice
• Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• Metal-insulator transition in a random Hubbard model
• Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade
• Influence of spin fluctuations near the Mott transition: a DMFT study
• Spin freezing and the Sachdev-Ye model
• One SYK SET
• Thermalization in different phases of charged SYK model
• Many-body energy invariant for $T$-linear resistivity
• Anomalous density fluctuations in a random $t$-$J$ model
• A Local Quantum Phase Transition in YFe${}_2$Al${}_{10}$
• On Planckian limit for inelastic relaxation in metals
• ω/T scaling of the optical conductivity in strongly correlated layered cobalt oxide
• Numerical solution of the t-J model with random exchange couplings in d=infinity dimensions
• Pairing by a dynamical interaction in a metal

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• A Criterion for Strange Metallicity in the Lorenz Ratio
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• 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
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