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Spread Complexity Rate as Proper Momentum
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We demonstrate a precise relation between the rate of complexity of quantum states excited by local operators in two-dimensional conformal field theories and the radial momentum of particles in 3-dimensional Anti-de Sitter spacetimes. Similar relations have been anticipated based on qualitative models for operator growth. Here, we make this correspondence sharp with two key ingredients: the precise definition of quantum complexity given by the spread complexity of states, and the match of its growth rate to the bulk momentum measured in the proper radial distance coordinate.
Forward citations
Cited by 23 Pith papers
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Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
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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 proper radial momenta of infalling particles in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
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Quantum scars from holographic boson stars
Mini-boson stars in AdS spacetime are proposed as holographic realizations of quantum scars, exhibiting chaotic spectra with integrable subsectors, anomalously low entanglement, and robust Krylov complexity revivals.
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Holographic Krylov Complexity for Charged, Composite and Extended Probes
Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
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Violation of Universal Operator Growth Hypothesis in $\mathcal{W}_3$Conformal Field Theories
In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in th...
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The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
A rescaled Wigner negativity in Krylov space grows as sinh^{4Δ} and, at Δ=1, its rate matches the tidal momentum of infalling geodesics in AdS3.
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The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
Normalized Krylov-Wigner negativity rate matches Krylov variance growth and equals tidal stretch rate R ∝ C P_ρ if and only if Δ=1 in AdS3.
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Wigner negativity in Krylov space and emergent semiclassicality
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
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Holographic Spread Complexity from Branes and Strings
D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
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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 of infalling particles in the BTZ black hole, providing a step toward generalizing the complexity-momentum correspondence.
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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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Quantum scars from holographic boson stars
Asymptotically AdS mini-boson stars exhibit scar-like states with random-matrix chaos signatures, embedded integrable branches, low entanglement, and Krylov complexity revivals, unlike thermal black holes.
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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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Complexity and Operator Growth in Holographic 6d SCFTs
In holographic 6d N=(1,0) SCFTs, generalized proper momentum of infalling particles grows linearly at late times, with early dynamics modified by SU(2)_R charge and quiver spreading.
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Krylov Complexity, Confinement and Universality
Holographic calculations show the proper-momentum proxy for Krylov complexity oscillates in every confining geometry with a smooth infrared cap, with frequency set by the confinement scale.
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Krylov Complexity of Supersymmetric SYK Models
In finite-size N=2 SYK, breaking supersymmetry with an irrelevant deformation pushes late-time Krylov complexity to roughly half the maximal Krylov-space bound, while a mass deformation leaves saturation complexity a ...
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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-ge...
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On the Universality of Probe Complexity in $\mathcal{N}=4$ SYM
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to t...
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Krylov complexity has it all
Krylov complexity is equivalent to Lanczos coefficients, return amplitude, and spectral density for operator dynamics, via an explicit recursive algorithm from its t=0 Taylor expansion.
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Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
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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-inte...
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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.
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