Time evolution of the complexity in chaotic systems: concrete examples

Abstract

We investigate the time evolution of the complexity of the operator by the Sachdev-Ye-Kitaev (SYK) model with $N$ Majorana fermions. We follow Nielsen's idea of complexity geometry and geodesics thereof. We show that it is possible that the bi-invariant complexity geometry can exhibit the conjectured time evolution of the complexity in chaotic systems: i) linear growth until $t\sim e^N$, ii) saturation and small fluctuations after then. We also show that the Lloyd's bound is realized in this model. Interestingly, these characteristic features appear only if the complexity geometry is the most natural "non-Riemannian" Finsler geometry. This serves as a concrete example showing that the bi-invariant complexity may be a competitive candidate for the complexity in quantum mechanics/field theory (QM/QFT). We provide another argument showing a naturalness of bi-invariant complexity in QM/QFT. That is that the bi-invariance naturally implies the equivalence of the right-invariant complexity and left-invariant complexity, either of which may correspond to the complexity of a given operator. Without bi-invariance, one needs to answer why only right (left) invariant complexity corresponds to the "complexity", instead of only left (right) invariant complexity.

arXiv commentpublished version

References in corpus (49)

• Comments on the Sachdev-Ye-Kitaev model
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Complexity, action, and black holes
• Quantum Computation as Geometry
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• The Second Law of Quantum Complexity
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On the Time Dependence of Holographic Complexity
• Holographic Complexity
• Noether charge, black hole volume, and complexity
• Complexity of Formation in Holography
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Quantum Computation vs. Firewalls
• Circuit Complexity in Fermionic Field Theory
• Complexity and entanglement for thermofield double states
• Complexity Growth for AdS Black Holes
• Quantum Complexity and Negative Curvature
• Complexity as a novel probe of quantum quenches: universal scalings and purifications
• On Volumes of Subregions in Holography and Complexity
• Path-Integral Complexity for Perturbed CFTs
• Black holes, complexity and quantum chaos
• Quantum Complexity of Time Evolution with Chaotic Hamiltonians
• Complexity and the bulk volume, a new York time story
• On Complexity for Higher Derivative Gravities
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -
• The effect of Dilaton on the holographic complexity growth
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• The boundary dual of the bulk symplectic form
• Evolution of Complexity Following a Global Quench
• Holographic subregion complexity under a thermal quench
• Strong energy condition and complexity growth bound in holography
• Principles and symmetries of complexity in quantum field theory
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Surface Counterterms and Regularized Holographic Complexity
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• Holographic complexity and action growth in massive gravities
• Action growth rate for a higher curvature gravitational theory
• Complexity of Holographic Superconductors
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Surface term, corner term, and action growth in F(Riemann) gravity theory
• More on complexity of operators in quantum field theory
• Thoughts on Holographic Complexity and its Basis-dependence
• Complexity of operators generated by quantum mechanical Hamiltonians

Cited by in corpus (23)

• Complexity growth of operators in the SYK model and in JT gravity
• Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
• Renormalized Circuit Complexity
• The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
• Complexity Growth in Integrable and Chaotic Models
• The Rise of Cosmological Complexity: Saturation of Growth and Chaos
• Circuit Complexity From Cosmological Islands
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
• Bounds on quantum evolution complexity via lattice cryptography
• Integrability and complexity in quantum spin chains
• Complexity for Open Quantum System
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Complexity factor for black holes in the framework of the Newman-Penrose formalism
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Complexity of non-trivial sound speed in inflation
• Towards the Web of Quantum Chaos Diagnostics
• Real space circuit complexity as a probe of phase diagrams
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• What kind of "complexity" is dual to holographic complexity?
• Benchmarking quantum chaos from geometric complexity
• Time-dependent Hamiltonians and Geometry of Operators Generated by Them
• Holographic Interpretation of Relative State Complexity