Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

Abstract

The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy limit.

arXiv comment38 pages, 6 figures

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Cited by in corpus (60)

• Towards a full solution of the large N double-scaled SYK model
• The bulk Hilbert space of double scaled SYK
• The Schwarzian Theory - A Wilson Line Perspective
• Universal chaotic dynamics from Krylov space
• Quantum Dynamics in Krylov Space: Methods and Applications
• Liouville quantum gravity -- holography, JT and matrices
• Defects in Jackiw-Teitelboim Quantum Gravity
• Fine Structure of Jackiw-Teitelboim Quantum Gravity
• A symmetry algebra in double-scaled SYK
• Krylov complexity in large-$q$ and double-scaled SYK model
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• The double scaled limit of Super--Symmetric SYK models
• von Neumann algebras in JT gravity
• Dynamical actions and q-representation theory for double-scaled SYK
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Pole skipping away from maximal chaos
• Quenched vs Annealed: Glassiness from SK to SYK
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Krylov fractality and complexity in generic random matrix ensembles
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Correlators of double scaled SYK at one-loop
• Krylov spread complexity as holographic complexity beyond JT gravity
• Going beyond ER=EPR in the SYK model
• The dilaton gravity hologram of double-scaled SYK
• Hartle-Hawking wavefunction in double scaled SYK
• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• Wormholes, branes and finite matrices in sine dilaton gravity
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Chaos on the hypercube
• Quantum gravity of the Heisenberg algebra
• $Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model
• Quantum exponentials for the modular double and applications in gravity models
• Effective description of sub-maximal chaos: stringy effects for SYK scrambling
• Chaos in Three-dimensional Higher Spin Gravity
• Soft modes in $\mathcal{N}=2$ SYK model
• Fundamental weight systems are quantum states
• Complexity is not Enough for Randomness
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Toward Krylov-based holography in double-scaled SYK
• Slow scrambling and hidden integrability in a random rotor model
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• D-commuting SYK model: building quantum chaos from integrable blocks
• Quantum group origins of edge states in double-scaled SYK
• Bulk Reconstruction from Generalized Free Fields
• Gravitational wavefunctions in JT supergravity
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality
• SYK Model with global symmetries in the double scaling limit
• Towards a String Dual of SYK
• Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry
• Quantum Annealing with chaotic driver Hamiltonians
• Two-local modifications of SYK model with quantum chaos
• Spectral Form Factor in Sparse SYK Models
• On perturbation around closed exclusion processes
• Bosonic near-CFT${}_1$ models from Fock-space fluxes
• A dynamical version of the SYK Model and the q-Brownian Motion
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
• Schur Connections: Chord Counting, Line Operators, and Indices
• Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p-spin interactions