A statistical mechanism for operator growth

Abstract

It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in $d\ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.

arXiv comment9 pages, 0 figures; v2: accepted version, minor revisions

References in corpus (32)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Many-body localization, thermalization, and entanglement
• Operator Spreading in Random Unitary Circuits
• On Many-Body Localization for Quantum Spin Chains
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Eigenstate Thermalization Hypothesis
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Integrals of motion in the Many-Body localized phase
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Exponentially slow heating in periodically driven many-body systems
• Quantum chaos challenges many-body localization
• A Universal Operator Growth Hypothesis
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Solution of a minimal model for many-body quantum chaos
• Thouless time analysis of Anderson and many-body localization transitions
• Does scrambling equal chaos?
• Probing quench dynamics across a quantum phase transition into a 2D Ising antiferromagnet
• Operator complexity: a journey to the edge of Krylov space
• On The Evolution Of Operator Complexity Beyond Scrambling
• Can we study the many-body localisation transition?
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Thouless energy and multifractality across the many-body localization transition
• Entanglement and matrix elements of observables in interacting integrable systems
• Bounds on chaos from the eigenstate thermalization hypothesis
• Floquet prethermalization in a Bose-Hubbard system
• Euclidean operator growth and quantum chaos
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Signature of quantum chaos in operator entanglement in 2d CFTs

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• Probing quantum scars and weak ergodicity-breaking through quantum complexity
• Eigenstate Thermalization Hypothesis and Free Probability
• Krylov complexity and orthogonal polynomials
• Operator growth in 2d CFT
• Thermalization of dilute impurities in one dimensional spin chains
• Krylov complexity in quantum field theory, and beyond
• Krylov complexity in large-$q$ and double-scaled SYK model
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Krylov complexity of density matrix operators
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Spectral and Krylov Complexity in Billiard Systems
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• Numerically Probing the Universal Operator Growth Hypothesis
• Assessing the saturation of Krylov complexity as a measure of chaos
• Krylov Complexity in Lifshitz-type Scalar Field Theories
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Inflationary Krylov complexity
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• The operator growth hypothesis in open quantum systems
• Universality classes of thermalization for mesoscopic Floquet systems
• Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics
• Quantum many-body simulations with PauliStrings.jl
• Measurable Krylov Spaces and Eigenenergy Count in Quantum State Dynamics
• Stochastic Sampling of Operator Growth Dynamics
• Approximation theory for Green's functions via the Lanczos algorithm
• Opening Krylov space to access all-time dynamics via dynamical symmetries
• Krylov Complexity Meets Confinement
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• Probing Krylov Complexity in Scalar Field Theory with General Temperatures
• Emergent random matrix universality in quantum operator dynamics
• Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
• Engineering Quantum Reservoirs through Krylov Complexity, Expressivity and Observability
• Krylov complexity of thermal state in early universe
• From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry