Dispersive SYK model: band structure and quantum chaos

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a concrete model for non-Fermi Liquid with maximally chaotic behavior in $0+1$-$d$. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by a constant hopping. We call this dispersive SYK model. Focusing on $1+1$-$d$ homogeneous hopping, by either tuning temperature or the relative strength of random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where dynamic exponent $z$ changes from $1$ to $\infty$. We study the crossover by calculating spectral function, charge density correlator and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a Van Hove singularity because of the large density of states near the Fermi suface. The effect of the topological non-trivial bands is also discussed.

arXiv comment9 pages, 9 figures

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• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Theory of a Planckian metal
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Magnetotransport in a model of a disordered strange metal
• Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-$1/2$ fermions
• Lindbladian dissipation of strongly-correlated quantum matter
• Transport and chaos in lattice Sachdev-Ye-Kitaev models
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Strange metal from local quantum chaos
• Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Coherent superconductivity with large gap ratio from incoherent metals
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Contrasting SYK-like Models
• Phases Of Melonic Quantum Mechanics
• Universal subdiffusion in strongly tilted many-body systems
• Towards the Holographic Dual of N = 2 SYK
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain
• Quantum criticality and duality in the SYK/AdS${}_2$ chain
• Intrinsic superconducting instabilities of a solvable model for an incoherent metal
• Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Topological Sachdev-Ye-Kitaev Model
• Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode
• Thickening and sickening the SYK model
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane
• Tunneling through an Eternal Traversable Wormhole
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models
• Deconfined critical point in a doped random quantum Heisenberg magnet
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Superconducting critical temperature in the extended diffusive SYK model
• Page Curve from Non-Markovianity
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
• One SYK SET
• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Collective density fluctuations of strange metals with critical Fermi surfaces
• Bad metallic transport in geometrically frustrated models
• Non-Fermi liquid behavior in the Sachdev-Ye-Kitaev model for a one dimensional incoherent semimetal
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• SYK does not Transit Gloria Mundi just yet
• Wormhole-induced effective coupling in SYK chains
• Mimicking black hole event horizons in atomic and solid-state systems
• Super-maximal chaos and instability
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
• Information scrambling and butterfly velocity in quantum spin glass chains
• More on Complex Sachdev-Ye-Kitaev Eternal Wormholes
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models