Quantum Entanglement of the Sachdev-Ye-Kitaev Models

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical model of fermions interacting with $q$-body random couplings. For $q=2$, it describes free particles, and is non-chaotic in the many-body sense, while for $q>2$ it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the SYK$q$ models, for a bipartition of $N$ real or complex fermions into subsystems containing $2m$ real/$m$ complex fermions and $N-2m$/$N-m$ fermions in the remainder. For the free model SYK$2$, we obtain an analytic expression for the EE, derived from the $\beta$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path integral formalism to show that the EE is {\em maximal} for when one subsystem is small, i.e. $m\ll N$, for {\em arbitrary} $q$. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e. $m/N$ is $O(1)$. Finally, we explore the EE for a model with both SYK2 and SYK4 interaction and find a crossover from SYK2 (low temperature) to SYK4 (high temperature) behavior as we vary energy.

9 pages, 5 figures; fixed typo in the title

References in corpus (3)

• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach

Cited by in corpus (72)

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• SYK meets non-Hermiticity II: measurement-induced phase transition
• Entanglement and matrix elements of observables in interacting integrable systems
• Ultra-stable charging of fast-scrambling SYK quantum batteries
• Quantum holography in a graphene flake with an irregular boundary
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• Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• The Page Curve for Fermionic Gaussian States
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Eigenstate entanglement in the Sachdev-Ye-Kitaev model
• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
• Symmetry-resolved Page curves
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Generalized Deep Thermalization for Free Fermions
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Spacetime from Unentanglement
• Charge transport in graphene-based mesoscopic realizations of Sachdev-Ye-Kitaev models
• An entanglement perspective on the quantum approximate optimization algorithm
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Generalized thermalization in quantum-chaotic quadratic Hamiltonians
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid
• Tight-binding billiards
• Can neural quantum states learn volume-law ground states?
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Scrambling via Braiding of Nonabelions
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Eigenstate thermalization scaling in approaching the classical limit
• Entanglement dualities in supersymmetry
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Thermalization of Randomly Coupled SYK Models
• Entropy Linear Response Theory with Non-Markovian Bath
• Non-Abelian entanglement asymmetry in random states
• Typical entanglement entropy in systems with particle-number conservation
• Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Wormholes and the Thermodynamic Arrow of Time
• Symmetry classification of typical quantum entanglement
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Characterizing quantum chaoticity of kicked spin chains
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• Mimicking black hole event horizons in atomic and solid-state systems
• Probing Entanglement Dynamics in the SYK Model using Quantum Computers
• Entanglement behavior and localization properties in monitored fermion systems
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Towards Entanglement Entropy of Random Large-N Theories
• Average mutual information for random fermionic Gaussian quantum states
• Volume-law entanglement entropy of typical pure quantum states
• Efficient computation of average subsystem Bures distance between fermionic Gaussian states
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Solvable random matrix ensemble with a logarithmic weakly confining potential
• Quantum entropy thermalization