In double-scaled SYK, state-adapted dressed chord operators change the emergent algebra from Type II1 to Type I∞ and restore purity of KM states, unlike generic operators.
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In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.
Krylov complexity's Taylor coefficients recursively determine all Lanczos coefficients, making it a complete descriptor of operator dynamics, with caveats for spread complexity.
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
citing papers explorer
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Emergent States and Algebras from the Double-Scaling limit of Pure States in SYK
In double-scaled SYK, state-adapted dressed chord operators change the emergent algebra from Type II1 to Type I∞ and restore purity of KM states, unlike generic operators.
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Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
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Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random matrix statistics.
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Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity
Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.
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Krylov complexity has it all
Krylov complexity's Taylor coefficients recursively determine all Lanczos coefficients, making it a complete descriptor of operator dynamics, with caveats for spread complexity.
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Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
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Toward Krylov-based holography in double-scaled SYK
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
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Towards a microscopic description of de Sitter dynamics
An SYK-based quantum system reproduces semiclassical correlators of quantum fields in rigid de Sitter space and non-trivial OTOC features including a doubled Lyapunov exponent.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
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Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity
Finite cutoff in JT gravity causes faster ERB-length saturation, deformation-dependent baby-universe emission only under Lorentzian evolution, and possible one-cut universality corrections in the matrix dual.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
- q-Askey Deformations of Double-Scaled SYK
- Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography