Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains

Abstract

We discuss the dynamics of integrable and nonintegrable chains of coupled oscillators under continuous weak position measurements in the semiclassical limit. We show that, in this limit, the dynamics is described by a standard stochastic Langevin equation, and a measurement-induced transition appears as a noise- and dissipation-induced chaotic-to-nonchaotic transition akin to stochastic synchronization. In the nonintegrable chain of anharmonically coupled oscillators, we show that the temporal growth and the ballistic light-cone spread of a classical out-of-time correlator characterized by the Lyapunov exponent and the butterfly velocity, are halted above a noise or below an interaction strength. The Lyapunov exponent and the butterfly velocity both act like order parameter, vanishing in the nonchaotic phase. In addition, the butterfly velocity exhibits a critical finite-size scaling. For the integrable model, we consider the classical Toda chain and show that the Lyapunov exponent changes nonmonotonically with the noise strength, vanishing at the zero noise limit and above a critical noise, with a maximum at an intermediate noise strength. The butterfly velocity in the Toda chain shows a singular behavior approaching the integrable limit of zero noise strength.

4p + eps Main text; 13p Supplementary

References in corpus (24)

• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Measurement-induced quantum criticality under continuous monitoring
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Universality of entanglement transitions from stroboscopic to continuous measurements
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Measurement-induced transitions of the entanglement scaling law in ultracold gases with controllable dissipation
• Entanglement Negativity at Measurement-Induced Criticality
• Measurements conspire nonlocally to restructure critical quantum states
• Entanglement growth in diffusive systems
• Classical many-body chaos with and without quasiparticles
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Quantum scrambling and the growth of mutual information
• Measurement-induced phase transition in a classical, chaotic many-body system
• Diffusive scaling of Rényi entanglement entropy
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach
• Arresting classical many-body chaos by kinetic constraints
• Butterfly Effect and Spatial Structure of Information Spreading in a Chaotic Cellular Automaton
• Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
• The $\hslash \to 0$ Limit of the Entanglement Entropy
• Constrained Dynamics and Directed Percolation
• A universal crossover in quantum circuits governed by a proximate classical error correction transition

Cited by in corpus (3)

• Measurement-induced phase transition in periodically driven free-fermionic systems
• Inverse Superconductor-Insulator Transition in Weakly Monitored Josephson Junction Arrays
• Long-time signatures of chaos in large atom-light frequency ratios Rabi model