Krylov complexity in large-$q$ and double-scaled SYK model

Abstract

Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The Krylov complexity naturally describes the "size" of the distribution, while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK${}_q$ at infinite temperature, where $q\sim \sqrt{N}$. In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be "hyperfast", which is previously conjectured to be associated with scrambling in de Sitter space.

v4: minor changes, published version in JHEP

References in corpus (13)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• A Generalization of Sachdev-Ye-Kitaev
• Krylov complexity from integrability to chaos
• Operator growth and Krylov construction in dissipative open quantum systems
• Krylov Localization and suppression of complexity
• The bulk Hilbert space of double scaled SYK
• Probing quantum scars and weak ergodicity-breaking through quantum complexity
• Krylov Complexity in Open Quantum Systems
• Spread Complexity and Topological Transitions in the Kitaev Chain
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• The growth of operator entropy in operator growth
• Spectral form factor in the double-scaled SYK model

Cited by in corpus (30)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov complexity in quantum field theory, and beyond
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Dynamical actions and q-representation theory for double-scaled SYK
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• Krylov complexity as an order parameter for quantum chaotic-integrable transitions
• Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
• Krylov Delocalization/Localization across Ergodicity Breaking
• The dilaton gravity hologram of double-scaled SYK
• Operator growth and spread complexity in open quantum systems
• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• Krylov complexity for non-local spin chains
• Krylov Complexity in Mixed Phase Space
• Krylov complexity of deformed conformal field theories
• Complexity = Anything Can Grow Forever in de Sitter
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
• Operator size growth in Lindbladian SYK
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Toward Krylov-based holography in double-scaled SYK
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• Stochastic Sampling of Operator Growth Dynamics
• Quantum group origins of edge states in double-scaled SYK
• Krylov Complexity in the Schrödinger Field Theory
• Notes on Wormhole Cancellation and Factorization
• Probing Krylov Complexity in Scalar Field Theory with General Temperatures
• Universal Time Evolution of Holographic and Quantum Complexity
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory