Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
arXiv:2407.21793 · doi:10.1088/1751-8121/ad91fd
Abstract
Symmetry resolved entanglement and entanglement asymmetry are two measures of quantum correlations sensitive to symmetries of the system. Here we discuss their non-equilibrium dynamics in the Rule 54 cellular automaton, a simple, yet interacting, integrable model. Both quantities can be expressed in terms of the more analytically tractable "charged moments", i.e. traces of powers of a suitably deformed density matrix, via a replica trick. We express them in terms of a tensor network, which we contract in space using a system of local algebraic relations. This gives the asymptotic form for the charged moments, valid in the regime of large but finite time that is shorter than all the relevant subsystem sizes. In this regime the charge moments decay exponentially with the rate given by the leading solution to a cubic equation.
21 pages, 2 figures; Submitted to the special issue of Journal of Physics A: Mathematical and Theoretical, "Quantum-Circuit Models for Many-Body Physics Out of Equilibrium"; v2 accepted version
References in corpus (31)
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Postselection-free entanglement dynamics via spacetime duality
- Matrix Product States for dynamical simulation of infinite chains
- Entanglement asymmetry as a probe of symmetry breaking
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
- Entanglement and symmetry resolution in two dimensional free quantum field theories
- Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
- Microscopic origin of the quantum Mpemba effect in integrable systems
- Symmetry-resolved dynamical purification in synthetic quantum matter
- Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
- Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
- Entanglement barrier and its symmetry resolution: theory and experiment
- Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
- Connecting Entanglement in Time and Space: Improving the Folding Algorithm
- Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
- Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
- Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
- Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
- Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
- Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
- Dynamics of charge fluctuations from asymmetric initial states
- Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
- Scaling of temporal entanglement in proximity to integrability
- A universal formula for the entanglement asymmetry of matrix product states
- Exact matrix product decay modes of a boundary driven cellular automaton
- Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
- Integrable deformations of superintegrable quantum circuits
- Symmetry Resolution in non-Lorentzian Field Theories
- Entanglement dynamics of thermofield double states in integrable models
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- The quantum Mpemba effects
- Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
- Measurement-induced symmetry restoration and quantum Mpemba effect
- Quantum Mpemba effect without global symmetries
- Entanglement asymmetry and symmetry defects in boundary conformal field theory
- A simpler probe of the quantum Mpemba effect in closed systems
- Entanglement asymmetry dynamics in random quantum circuits
- Quantum Mpemba effect in long-range spin systems
- Symmetry breaking in chaotic many-body quantum systems at finite temperature
- Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
- Non-Abelian entanglement asymmetry in random states
- Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
- Dynamics of entanglement fluctuations and quantum Mpemba effect in the QSSEP model
- Breaking global symmetries with locality-preserving operations
- Phase transition from localization to chaos in classical many-body system
- Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench