Numerical study of fermion and boson models with infinite-range random interactions

Abstract

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the $N$-site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of $N=\infty$ saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing temperature. The exact diagonalization results for the fermion Green's function also appear to converge well to the $N=\infty$ solution. For the hard-core boson model, the exact diagonalization study indicates spin glass order. Some results on the entanglement entropy and the out-of-time-order correlators are also presented.

20 pages, 10 figures; v2: more references, minor changes

References in corpus (1)

• Strange metals and the AdS/CFT correspondence

Cited by in corpus (162)

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• Higher Dimensional Generalizations of the SYK Model
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• Out-of-Time-Order Correlation at a Quantum Phase Transition
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• A Supersymmetric SYK-like Tensor Model
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Quantum holography in a graphene flake with an irregular boundary
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Three Dimensional View of the SYK/AdS Duality
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• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
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• Dispersive SYK model: band structure and quantum chaos
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Random Matrices and Holographic Tensor Models
• Pure states in the SYK model and nearly-$Ad{S}_2$ gravity
• Space-Time in the SYK Model
• Eigenstate entanglement in the Sachdev-Ye-Kitaev model
• Topological Quantum Liquids with Long-Range Couplings
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Three Dimensional View of Arbitrary $q$ SYK models
• Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
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• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
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• Symmetry Breaking in Coupled SYK or Tensor Models
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• A critical strange metal from fluctuating gauge fields in a solvable random model
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Diffusion in higher dimensional SYK model with complex fermions
• Entanglement Features of Random Hamiltonian Dynamics
• Diagnosing quantum chaos in many-body systems using entanglement as a resource
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
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• Spacetime from Unentanglement
• Disorder in the Sachdev-Yee-Kitaev Model
• Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
• $T$-linear resistivity in models with local self-energy
• Periodic Table of SYK and supersymmetric SYK
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
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• Fast scrambling without appealing to holographic duality
• $Ad{S}_2$ dilaton gravity from reductions of some nonrelativistic theories
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Binary-coupling sparse SYK: an improved model of quantum chaos and holography
• Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems
• On thermalization in the SYK and supersymmetric SYK models
• Yukawa-SYK model and Self-tuned Quantum Criticality
• Replica-nondiagonal solutions in the SYK model
• Quenched vs Annealed: Glassiness from SK to SYK
• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
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• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
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• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
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• Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model
• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
• Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions
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• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
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• Revealing nonperturbative effects in the SYK model
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• Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Entanglement behavior and localization properties in monitored fermion systems
• Quantum simulations of complex systems
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• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Theoretical Properties of Entropy in a Strong Coupling Region
• From eigenstate thermalization to hydrodynamic transport in correlated metals
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