We investigate the bulk-boundary correspondence in the SYK model from a quantum information perspective. The SYK model describes a system of Majorana fermions with random all-to-all interactions, whose disorder average-typically taken over a Gaussian ensemble-admits a dual description in terms of JT gravity in the large-$N$, low-energy limit. This framework provides a minimal setting for exploring holography and emergent spacetime in nearly AdS$_2$. We probe the holographic principle through diagnostics of quantum chaos and entanglement. In the early-time regime, the SYK model saturates the universal bound on the Lyapunov exponent, signaling maximal chaos consistent with semiclassical black hole dynamics. In the late-time regime, its spectral statistics are governed by random matrix theory, reflecting universal features of strongly chaotic quantum systems. These dynamical properties establish a concrete link between boundary quantum chaos and bulk semiclassical gravity. In parallel, we analyze quantum entanglement and the structure of operator algebras to investigate transitions in the associated von Neumann algebras and their implications for emergent geometry. To explore the robustness of these phenomena, we consider deformations of the SYK model through modified matter couplings and alternative random distributions. Our results clarify how quantum information-theoretic structures encode bulk gravitational dynamics and provide insight into the mechanism of spacetime emergence.
We investigate the bulk-boundary correspondence in the SYK model from a quantum information perspective. The SYK model describes a system of Majorana fermions with random all-to-all interactions, whose disorder average-typically taken over a Gaussian ensemble-admits a dual description in terms of JT gravity in the large-N, low-energy limit. This framework provides a minimal setting for exploring holography and emergent spacetime in nearly AdS2. We probe the holographic principle through diagnostics of quantum chaos and entanglement. In the early-time regime, the SYK model saturates the universal bound on the Lyapunov exponent, signaling maximal chaos consistent with semiclassical black hole dynamics. In the late-time regime, its spectral statistics are governed by random matrix theory, reflecting universal features of strongly chaotic quantum systems. These dynamical properties establish a concrete link between boundary quantum chaos and bulk semiclassical gravity. In parallel, we analyze quantum entanglement and the structure of operator algebras to investigate transitions in the associated von Neumann algebras and their implications for emergent geometry. To explore the robustness of these phenomena, we consider deformations of the SYK model through modified matter couplings and alternative random distributions. Our results clarify how quantum information-theoretic structures encode bulk gravitational dynamics and provide insight into the mechanism of spacetime emergence.
We model backreaction in AdS 2 JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography .
This enhanced Version II presents the SYK TENSOR Quantum Information Network(QIN) as a complete, finite, and empirically validated theory of quantum gravity. Realityemerges from a discrete, finite capacity substrate of maximally chaotic Majorana qubitsgoverned by random all to all SYK interactions, stabilized by holographic tensor networkerror correction, and regulated softly with Gaussian form factors to achieve bounded UVentanglement variance. Large scale numerical experiments (N = 8–64 qubits, Hilbert dimension up to 232) confirm four sharp, falsifiable predictions with refined precision: (1)maximal chaos scrambling quantified by Lyapunov exponent λL = 0.85 ± 0.12, (2) holographic bulk reconstruction with Ryu-Takayanagi correlation ρ = 0.68±0.12, (3) resolutionof the black hole information paradox via traversable wormhole teleportation achieving fidelity F = 0.4021±0.168 (6.43× classical advantage, paired t-test p = 4.4×10−12), and (4)emergent gravity scaling with strong anticorrelation r = −0.94 between chaos rate and effective gravitational coupling. An exact OTOC derivation through the Jackiw-Teitelboim (JT)gravity duality in nearly AdS2, bounded variance in regulated entanglement entropy withstability coefficient γ = 1, and rigorous derivation of the Einstein field equations from scrambling backreaction establish mathematical consistency. The framework naturally eliminatesUVdivergences, derives spacetime geometry and gravitational dynamics from pre-geometricquantum information flow, and provides direct pathways for Planck scale simulation onnear term quantum hardware (N > 100 logical qubits). Comparisons with loop quantumgravity and string theory highlight the QIN’s unique advantages in solvability, maximalchaos, and empirical accessibility. This work represents a groundbreaking unification ofquantum mechanics and gravity without continuum assumptions, extra dimensions, or adhoc fields.
Recent years have witnessed tremendous progress in developing a fine-grained low-dimensional holographic correspondence, specifically the construction of quantum mechanical boundary theories as holographic duals of two-dimensional gravity. In these developments, quantum chaos played a crucial role, both as source of universality and as a guiding principle for the matching of bulk and boundary signatures of gravity. In this article we review the construction of the chaos-assisted low-dimensional holographic correspondence for non-experts. We open with an introductory discussion of the two main protagonists of the theory, the SYK model and two-dimensional Jackiw-Teitelboim gravity. Within this framework we will discuss two independent 'bridges' between bulk and boundary physics, one pertaining to early time chaotic instabilities, the other to late time quantum chaos up to and including time scales of the order of the gravitational quantum level spacing. We will demonstrate that the resolution of these fine-grained quantum scales requires the extension of semiclassical gravity by elements of string theory. We conclude with an outlook towards higher dimensional generalizations of the chaotic holographic correspondence.
A bstract The Sachdev-Ye-Kitaev (SYK) model is a system of N Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1 −p . Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian’s eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio r (characterizing the distribution of gaps between consecutive eigenvalues). We find that when p is greater than a transition value p 1 , which scales as 1/ N 3 , both the SFF and r match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for p < p 1 , deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value p 2 , which also scales as 1/ N 3 , even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.
This is the thrid paper of the series of three: Spacetime and Gravity as Emergent Quantum Entanglement — A Proof of Concept The paper closes the three principal open questions of the series by identifying the physical boundary Hamiltonian, fixing all free thermodynamic parameters, and establishing that the boundary theory is maximally chaotic. Four results are proved: Theorem A identifies the boundary Hamiltonian as the Sachdev–Ye–Kitaev model: an explicit Collins–Śniady Weingarten calculation applied to the binary tree encoder's unitary 2-design property shows that the tree ensemble average and the SYK disorder average produce identical Gaussian coupling variance at leading order in 1/χ, yielding the same Schwinger–Dyson equations and the same conformal Green function G(τ) = −b·J⁻¹/²·sgn(τ)/|τ|¹/², establishing H_R = H_SYK as an equality of disorder-averaged effective field theories. Theorem B derives the previously free Schwarzian coefficient and topological dilaton — φ_r = (πb²N/16J)·log(J/Δ) and φ_0 = N/(2log₂χ) — making the near-extremal black hole entropy a parameter-free prediction. Theorem C proves that the quantum Lyapunov exponent saturates the Maldacena–Shenker–Stanford chaos bound at λ_L = 2πT, with scrambling time t* ~ β log N, placing the boundary theory in the fast-scrambling and GUE random-matrix universality class. Theorem D confirms the boundary stress-tensor two-point function ⟨T(x)T(0)⟩ = 6log₂χ/(2x²) as an unconditional theorem, consistent with an effective central charge c_eff = 6log₂χ. A corollary shows that the Bisognano–Wichmann assumption of Paper II is unnecessary once the explicit boundary Hamiltonian is in hand. Together with Papers I and II, this paper completes the derivation of the full holographic dictionary for the binary tree model — from a discrete quantum network to emergent geometry, physical time, gravitational field equations, and quantum chaos — entirely from first principles.
This dissertation presents a comprehensive investigation of fermionic quantum matter into the intricate relationship between quantum chaos, thermalization, and their connection to gravitational duals, with particular emphasis on the Sachdev-Ye-Kitaev (SYK) model and its extensions. Through an integrated approach combining analytical solutions in the large-N limit with advanced numerical techniques, we explore fundamental questions in quantum many-body physics, including the interplay of chaos and ergodicity, universal transport in non-Fermi liquids, and the role of gravitational analogs in strongly correlated systems. We first demonstrate that coupled SYK lattices evade instantaneous thermalization despite weak charge fluctuations, governed by a discrete wave equation dependent solely on hopping strength, independent of on-site interactions. Thermodynamically, coupled SYK models exhibit critical exponents universal to van der Waals fluids and AdS black holes, yet diverge from the Hawking-Page transition at ultralow temperatures, revealing a continuum of first-order phase transitions. They simultaneously retain the quantum chaotic properties of both a single-dot SYK model and black holes. In extended SYK chains, we identify a universal DC conductivity bound across interaction regimes, identifying crossovers between insulating, Fermi liquid, strange metal, and bad metal phases with signatures of holographic insulator behavior. Quench dynamics in mixed SYK systems reveal rapid thermalization without prethermal plateaus, enabling direct observation of thermalization in closed quantum systems in the thermodynamic limit. To diagnose ergodicity-breaking, we introduce the Krylov variance, a probe of operator localization in Krylov space, validated through mass-deformed SYK and quantum East models. Finally, we uncover Page curve entanglement dynamics and temporal quantum phase transitions in entanglement Hamiltonians of interacting fermionic chains, where symmetry-sector crossings highlight limitations of perturbative calculations performed around initial times, such as in Hawking’s analysis of black hole evaporation. We provide a condensed matter analog of the holographic “island formula” — a mechanism invoking quantum extremal surfaces to resolve the black hole information paradox. Methodologically, this work integrates large-N-type expansions, Keldysh contour techniques, and numerical methods to bridge condensed matter physics, quantum information, and gravitational duality. The results establish SYK-type systems as a universal framework for studying non-Fermi liquids, quantum criticality, and black hole analogs, while paving the way for exploring bosonic extensions and generalizations to open quantum systems.