Multi-Region Entanglement in Locally Scrambled Quantum Dynamics

Abstract

We study the evolution of multi-region bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multi-region entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a novel theoretical framework, called the entanglement feature formalism, to organize all the multi-region entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multi-region entanglement features. Using these tools, we are able to study the multi-region entanglement dynamics jointly and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement feature Hamiltonian. Depending on the quantum dynamics model, we find that multi-region effects can dominate the single region entanglement growth and only vanish for Haar random circuits. We calculate the operator-averaged out-of-time-order correlator based on the entanglement feature Hamiltonian and extract the butterfly velocity from the result. We show that the previously conjectured bound between the entanglement velocity and the butterfly velocity holds true even under the influence of multi-region entanglement. These developments could enable more efficient numerical simulations and more systematic theoretical understandings of the multi-region entanglement dynamics in quantum many-body systems.

23 pages, 15 figures; added & updated references

References in corpus (70)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Entanglement spectrum of a topological phase in one dimension
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum thermalization through entanglement in an isolated many-body system
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Chaos in quantum channels
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Measurement-driven entanglement transition in hybrid quantum circuits
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Towards the fast scrambling conjecture
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• A Universal Operator Growth Hypothesis
• Dynamics of quantum entanglement
• Periodically driven ergodic and many-body localized quantum systems
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Out-of-Time-Order Correlation for Many-Body Localization
• Solution of a minimal model for many-body quantum chaos
• Entanglement transition from variable-strength weak measurements
• Emergent statistical mechanics of entanglement in random unitary circuits
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Entanglement Transitions from Holographic Random Tensor Networks
• Operator space entanglement entropy in transverse Ising chain
• Hilbert-Space Fragmentation from Strict Confinement
• On entanglement spreading in chaotic systems
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Onset of Random Matrix Behavior in Scrambling Systems
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Locality, Quantum Fluctuations, and Scrambling
• Entanglement dynamics in quantum many-body systems
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Quantum thermalization dynamics with Matrix-Product States
• Machine Learning Spatial Geometry from Entanglement Features
• Operator Dynamics in Brownian Quantum Circuit
• Membrane theory of entanglement dynamics from holography
• Finite size scaling bounds on many-body localized phase transitions
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state
• Entanglement Features of Random Hamiltonian Dynamics
• Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
• Signature of quantum chaos in operator entanglement in 2d CFTs
• Measurement-Driven Phase Transition within a Volume-Law Entangled Phase
• Entanglement and the Sign Structure of Quantum States
• The Speed of Quantum Information Spreading in Chaotic Systems
• Entanglement growth after inhomogenous quenches
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Chaos and High Temperature Pure State Thermalization
• Measuring operator size growth in quantum quench experiments
• Random-matrix perspective on many-body entanglement with a finite localization length

Cited by in corpus (9)

• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Scalable and Flexible Classical Shadow Tomography with Tensor Networks
• Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• Dual-unitary shadow tomography
• Holographic Classical Shadow Tomography
• Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport