Butterflies from Information Metric

Abstract

We study time evolution of distance between thermal states excited by local operators, with different external couplings. We find that growth of the distance implies growth of commutators of operators, signifying the local excitations are scrambled. We confirm this growth of distance by holographic computation, by evaluating volume of codimension 1 extremal volume surface. We find that the distance increases exponentially as $e^{\frac{2\pi t}{\beta }}$. Our result implies that, in chaotic system, trajectories of excited thermal states exhibit high sensitivity to perturbation to the Hamiltonian, and the distance between them will be significant at the scrambling time. We also confirm the decay of two point function of holographic Wilson loops on thermofield double state.

10 pages, 3 figures, reference added, minor modifications

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Cited by in corpus (12)

• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Weak Quantum Chaos
• Universality in Chaos of Particle Motion near Black Hole Horizon
• Path-Integral Complexity for Perturbed CFTs
• Chaos and Complexity in Quantum Mechanics
• Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
• Scattering effect on entanglement propagation in RCFTs
• Chaos and Complexity for Inverted Harmonic Oscillators
• Out-of-Time-Ordered Correlators in $(T^2{)}^n/{\mathbb{Z}}_n$
• Non-perturbative Overlaps in JT Gravity: From Spectral Form Factor to Generating Functions of Complexity
• Universal Time Evolution of Holographic and Quantum Complexity
• Holographic Interpretation of Relative State Complexity