Low-rank Sachdev-Ye-Kitaev models

Abstract

Motivated by recent works on atom-cavity realizations of fast scramblers, and on Cooper pairing in non-Fermi liquids, we study a family of solvable variants of the ($q=4$) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate {an extensively degenerate or negative semidefinite coupling matrix}. More generic distributions give rise to "almost Fermi liquids" with a scaling dimension $\Delta =1/2$, but which differ from a genuine Fermi-liquid in quasi-particle decay rate, quantum Lyapunov exponent and/or specific heat.

arXiv comment5+10 pages, 10 figures

References in corpus (35)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Coupling Superconducting Qubits via a Cavity Bus
• Implementation of Cavity Squeezing of a Collective Atomic Spin
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Photon-mediated interactions between distant artificial atoms
• Traversable Wormholes via a Double Trace Deformation
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Bekenstein-Hawking Entropy and Strange Metals
• Measuring the scrambling of quantum information
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• A Universal Operator Growth Hypothesis
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Eternal traversable wormhole
• Cavity Mediated Collective Spin Exchange Interactions in a Strontium Superradiant Laser
• Bi-Local Holography in the SYK Model
• Dicke quantum spin glass of atoms and photons
• Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Quantum holography in a graphene flake with an irregular boundary
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Supermode-Density-Wave-Polariton Condensation
• Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition
• Transport and chaos in lattice Sachdev-Ye-Kitaev models
• Symmetry Breaking in Coupled SYK or Tensor Models
• A cavity-QED simulator of slow and fast scrambling
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Integrable and chaotic dynamics of spins coupled to an optical cavity
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• The chiral SYK model
• Dynamical thermalization in isolated quantum dots and black holes
• Quantum many-body dynamics on the star graph

Cited by in corpus (24)

• Ultra-stable charging of fast-scrambling SYK quantum batteries
• Protecting Spin Coherence in a Tunable Heisenberg Model
• Quantum Phase Transition in the Yukawa-SYK Model
• Dirac Fast Scramblers
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Yukawa-SYK model and Self-tuned Quantum Criticality
• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• Scrambling versus relaxation in Fermi and non-Fermi liquids
• $\text{Draiding}$ majoranas to dynamically engineer Hamiltonians
• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Quantum chaos and phase transition in the Yukawa-SYK model
• Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• Solvable Theory of a Strange Metal at the Breakdown of a Heavy Fermi Liquid
• Approximate Quantum Codes From Long Wormholes
• Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Electronic properties of the boson mode in a three-point fermion loop and the emergent SYK physics
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal