Analytic Spread Complexity from Level Statistics: From Chaos to Integrability

arXiv:2608.07412 · hep-th, cond-mat.stat-mech, quant-ph · Submitted 2026-08-07 · Read on arXiv

hep-th, cond-mat.stat-mech, quant-ph

Submitted: 2026-08-07

Updated: 2026-09-17

Code: https://github.com/pallabbasu/KrylovKernel

Terminology

• Krylov Complexity — 21× in this paper · explained in 3 episodes
• SYK Model — 7× in this paper · explained in 2 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Chaotic Dynamics — 2× in this paper · explained in 2 episodes
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Gaussian Orthogonal Ensemble — 1× in this paper
• Gaussian Unitary Ensemble — 1× in this paper
• Generalization — 1× in this paper · explained in 13 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Black holes and the butterfly effect
• A bound on chaos
• Black Holes and Random Matrices
• A Universal Operator Growth Hypothesis
• Quantum chaos and the complexity of spread of states
• Krylov complexity in conformal field theory
• Krylov complexity in quantum field theory, and beyond
• Krylov complexity and chaos in quantum mechanics
• Spectral and Krylov Complexity in Billiard Systems
• Time evolution of spread complexity and statistics of work done in quantum quenches
• Quantum state complexity meets many-body scars
• Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Spread complexity and quantum chaos for periodically driven spin chains
• Spread complexity in saddle-dominated scrambling
• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Krylov fractality and complexity in generic random matrix ensembles
• Complexity of Quadratic Quantum Chaos
• Chaos and integrability in triangular billiards
• Holographic Spread Complexity from Branes and Strings

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