Krylov complexity in saddle-dominated scrambling
arXiv:2203.03534 · doi:10.1007/JHEP05(2022)174
Abstract
In semi-classical systems, the exponential growth of the out-of-timeorder correlator (OTOC) is believed to be the hallmark of quantum chaos. However,on several occasions, it has been argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.
arXiv commentv3: few typos corrected, published version in JHEP
References in corpus (54)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- Operator Spreading in Random Unitary Circuits
- Localized shocks
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Two-dimensional conformal field theory and the butterfly effect
- Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
- A Universal Operator Growth Hypothesis
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Lieb-Robinson and the butterfly effect
- Out-of-Time-Order Correlation for Many-Body Localization
- Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
- Out-of-time-order correlators in quantum mechanics
- Does scrambling equal chaos?
- Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
- Scrambling and entanglement spreading in long-range spin chains
- Operator complexity: a journey to the edge of Krylov space
- Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
- On The Evolution Of Operator Complexity Beyond Scrambling
- Krylov complexity in conformal field theory
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Toda chain flow in Krylov space
- Krylov Localization and suppression of complexity
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Chaos and Complexity in Quantum Mechanics
- Complexity growth of operators in the SYK model and in JT gravity
- Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
- Euclidean operator growth and quantum chaos
- Reversible quantum information spreading in many-body systems near criticality
- Random Matrix Theory for Complexity Growth and Black Hole Interiors
- Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
- Operator Delocalization in Quantum Networks
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- Operator growth in 2d CFT
- Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
- Out-of-time-order Operators and the Butterfly Effect
- Scrambling without chaos in RCFT
- Probing excited-state quantum phase transition in a quantum many body system via out-of-time-ordered correlator
- Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
- Universal level statistics of the out-of-time-ordered operator
- Dynamics of almost strong edge modes in spin chains away from integrability
- A statistical mechanism for operator growth
- Out-of-time-order correlator in coupled harmonic oscillators
- Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
- Conformal field theory and the web of quantum chaos diagnostics
- Pedagogical introduction to SYK model and 2D Dilaton Gravity
- Saddle-point scrambling without thermalisation
- Quantum operator growth bounds for kicked tops and semiclassical spin chains
- The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models
- Subleading Bounds on Chaos
- Thermalization and its Breakdown for a Large Nonlinear Spin
- Extremal Chaos
- On the exact solutions of the Lipkin-Meshkov-Glick model
- Notes on Scrambling in Conformal Field Theory
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- Spread Complexity and Topological Transitions in the Kitaev Chain
- Krylov complexity in quantum field theory, and beyond
- Krylov complexity in large- and double-scaled SYK model
- Coherence requirements for quantum communication from hybrid circuit dynamics
- Quantum chaos, scrambling and operator growth in deformed SYK models
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
- Assessing the saturation of Krylov complexity as a measure of chaos
- Entanglement and geometry from subalgebras of the Virasoro algebra
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- Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain
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