Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment

Abstract

In closed generic many-body systems, unitary evolution disperses local quantum information into highly non-local objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the operator size growth. However, for quantum systems embedded in an environment, how the couplings to the environment affect the process of information scrambling quests revelation. Here we predict a dynamical transition in quantum systems with all-to-all interactions accompanied by an environment, which separates two phases. In the dissipative phase, information scrambling halts as the operator size decays with time, while in the scrambling phase, dispersion of information persists and the operator size grows and saturates to an $O(N)$ value in the long-time limit with $N$ the number of degrees of freedom of the systems. The transition is driven by the competition between the system intrinsic and environment propelled scramblings and the environment induced dissipation. Our prediction is derived from a general argument based on epidemiological models and demonstrated analytically via solvable Brownian SYK models. We provide further evidence which suggests that the transition is generic to quantum chaotic systems when coupled to an environment. Our study sheds light on the fundamental behavior of quantum systems in the presence of an environment.

6 pages + supplementary material

References in corpus (14)

• Black holes as mirrors: quantum information in random subsystems
• Information Scrambling in Computationally Complex Quantum Circuits
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Operator growth and Krylov construction in dissipative open quantum systems
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• A two-way approach to out-of-time-order correlators
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Subleading Weingartens
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Scrambling Ability of Quantum Neural Networks Architectures
• Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR
• Dynamics of quantum information scrambling under decoherence effects measured via active spins clusters
• Operator growth bounds in a cartoon matrix model

Cited by in corpus (12)

• Quantum Dynamics in Krylov Space: Methods and Applications
• On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Operator size growth in Lindbladian SYK
• Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators