Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics

Abstract

The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of an matrix product density operator (MPDO) representation of the density matrix in the tensor-network methods and provides a measure for the corresponding classical simulability. One example is the $\mathrm{U}(1)$-symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated $\mathrm{SU}(2)$ symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement also increases again in a logarithmic manner at late times in the $\mathrm{SU}(2)$-symmetric case. We find that this behavior can be fully understood from the corresponding $\mathrm{U}(1)$ subsymmetry by considering the symmetry-resolved operator entanglement. But unlike the $\mathrm{U}(1)$-symmetric case with dephasing, both the classical Shannon entropy associated with the probabilities for the half system being in different symmetry sectors and the corresponding symmetry-resolved operator entanglement have nontrivial contributions to the late time logarithmic growth of operator entanglement. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with $\mathrm{U}(1)$ as the symmetry or subsymmetry and for more broad dissipations beyond dephasing. By breaking the $\mathrm{SU}(2)$ symmetry of our quantum many-body dynamics to $\mathrm{U}(1)$, we also show that the latter property is valid even for open quantum systems with only $\mathrm{U}(1)$ symmetry.

Author's accepted manuscript

References in corpus (58)

• Many-Body Physics with Ultracold Gases
• A computable measure of entanglement
• The density-matrix renormalization group in the age of matrix product states
• Nonequilibrium dynamics of closed interacting quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Many-body localization, thermalization, and entanglement
• 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
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• The logarithmic negativity: A full entanglement monotone that is not convex
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Atomic quantum gases in periodically driven optical lattices
• Observation of a Discrete Time Crystal
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Quantum many-body scars
• Many-body localization in a quantum simulator with programmable random disorder
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Time-evolution methods for matrix-product states
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Probing entanglement in a many-body-localized system
• Entanglement and thermodynamics after a quantum quench in integrable systems
• The iTEBD algorithm beyond unitary evolution
• Entropy scaling and simulability by Matrix Product States
• On the Entangling Power of Quantum Evolutions
• Non-standard Hubbard models in optical lattices: a review
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Entanglement of Quantum Evolutions
• Symmetry-resolved entanglement in many-body systems
• Operator space entanglement entropy in transverse Ising chain
• A positive tensor network approach for simulating open quantum many-body systems
• Equipartition of the Entanglement Entropy
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Rényi generalization of the operational entanglement entropy
• Operator Space Entanglement Entropy in XY Spin Chains
• Superuniversality of superdiffusion
• Operationally accessible entanglement of one dimensional spinless fermions
• Strongly interacting ultracold polar molecules
• Quantum entanglement of unitary operators on bi-partite systems
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• Stability of superdiffusion in nearly integrable spin chains
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Entanglement barrier and its symmetry resolution: theory and experiment
• Non-Abelian symmetry can increase entanglement entropy
• Hilbert Space Fragmentation in Open Quantum Systems
• Absence of superdiffusion in certain random spin models
• Symmetry enforced entanglement in maximally mixed states
• Highly entangled stationary states from strong symmetries
• More on symmetry resolved operator entanglement