Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum
arXiv:2212.14702 · doi:10.1007/JHEP05(2023)226
Abstract
We study a notion of operator growth known as Krylov complexity in free and interacting massive scalar quantum field theories in -dimensions at finite temperature. We consider the effects of mass, one-loop self-energy due to perturbative interactions, and finite ultraviolet cutoffs in continuous momentum space. These deformations change the behavior of Lanczos coefficients and Krylov complexity and induce effects such as the "staggering" of the former into two families, a decrease in the exponential growth rate of the latter, and transitions in their asymptotic behavior. We also discuss the relation between the existence of a mass gap and the property of staggering, and the relation between our ultraviolet cutoffs in continuous theories and lattice theories.
V4: Added a clarification about the numerical fitting of the growth rate of the Lanczos coefficients in Sec. 3.2. (See Eqs. 3.25-3.27 and above paragraphs)
References in corpus (24)
- Complexity and Shock Wave Geometries
- Quantum Computation as Geometry
- Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
- Quantum chaos and the complexity of spread of states
- Operator space entanglement entropy in transverse Ising chain
- Loschmidt Echo
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Krylov complexity from integrability to chaos
- Krylov complexity in saddle-dominated scrambling
- Operator growth and Krylov construction in dissipative open quantum systems
- Krylov Localization and suppression of complexity
- Does Complexity Equal Anything?
- Operator growth in open quantum systems: lessons from the dissipative SYK
- Operator Space Entanglement Entropy in XY Spin Chains
- Ultimate Speed Limits to the Growth of Operator Complexity
- Quantum complexity and topological phases of matter
- Krylov complexity and orthogonal polynomials
- Complexity Equals Anything II
- Spread Complexity and Topological Transitions in the Kitaev Chain
- Quantum chaos, scrambling and operator growth in deformed SYK models
- Probing the entanglement of operator growth
- Numerically Probing the Universal Operator Growth Hypothesis
- A precision test of averaging in AdS/CFT
- Q-curvature and Path Integral Complexity
Cited by in corpus (43)
- Universal chaotic dynamics from Krylov space
- Quantum Dynamics in Krylov Space: Methods and Applications
- On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
- Krylov complexity and chaos in quantum mechanics
- Krylov complexity in quantum field theory, and beyond
- Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
- Krylov complexity of density matrix operators
- Spectral and Krylov Complexity in Billiard Systems
- Spread complexity in saddle-dominated scrambling
- Quantum complexity in gravity, quantum field theory, and quantum information science
- State Dependence of Krylov Complexity in CFTs
- Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
- Spread complexity as classical dilaton solutions
- A relation between Krylov and Nielsen complexity
- Operator growth and Krylov Complexity in Bose-Hubbard Model
- Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
- Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
- Krylov fractality and complexity in generic random matrix ensembles
- Krylov complexity and Trotter transitions in unitary circuit dynamics
- Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
- Quantum dynamics in one and two dimensions via recursion method
- Krylov complexity for non-local spin chains
- Krylov Complexity of Open Quantum Systems: From Hard Spheres to Black Holes
- Krylov complexity of deformed conformal field theories
- Universal Hypothesis of Autocorrelation Function from Krylov Complexity
- Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
- Circuit Complexity for Carrollian Conformal (BMS) Field Theories
- Krylov Complexity as a Probe for Chaos
- Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
- Measurable Krylov Spaces and Eigenenergy Count in Quantum State Dynamics
- Exactly solvable models for universal operator growth
- Holographic Complexity and Phase Transition for AdS Black Holes
- Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
- Krylov Complexity in Lifshitz-type Dirac Field Theories
- Krylov Complexity in the Schrödinger Field Theory
- Probing Krylov Complexity in Scalar Field Theory with General Temperatures
- Engineering Quantum Reservoirs through Krylov Complexity, Expressivity and Observability
- Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
- Relaxation Fluctuations of Correlation Functions: Spin and Random Matrix Models
- From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
- Higher-Order Krylov State Complexity in Random Matrix Quenches
- Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry
- Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory