Rise and fall, and slow rise again, of operator entanglement under dephasing
arXiv:2201.05099 · doi:10.1103/PhysRevLett.129.170401
Abstract
The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a conservation law. We argue that in an XXZ spin-model and a Bose-Hubbard model the OE grows universally as at long times, and as for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.
arXiv comment4.5 + 7 pages, 3 + 4 figures
References in corpus (73)
- The density-matrix renormalization group in the age of matrix product states
- Quantum Simulation
- Area laws for the entanglement entropy - a review
- 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
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Many body localization in Heisenberg XXZ magnet in a random field
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- Quantum trajectories and open many-body quantum systems
- Quantum Zeno Effect and the Many-body Entanglement Transition
- 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
- Unitary-projective entanglement dynamics
- Entropy scaling and simulability by Matrix Product States
- On the Entangling Power of Quantum Evolutions
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Rydberg atom quantum technologies
- Quantum simulation and computing with Rydberg-interacting qubits
- Entanglement of Quantum Evolutions
- Symmetry-resolved entanglement in many-body systems
- Algebraic versus exponential decoherence in dissipative many-particle systems
- Simulation methods for open quantum many-body systems
- Operator space entanglement entropy in transverse Ising chain
- Relaxation times of dissipative many-body quantum systems
- A positive tensor network approach for simulating open quantum many-body systems
- Equipartition of the Entanglement Entropy
- Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Measurement-induced dark state phase transitions in long-ranged fermion systems
- Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
- Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect
- From random walk to single-file diffusion
- Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
- Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
- Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
- Growth of entanglement entropy under local projective measurements
- Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
- Interaction-induced impeding of decoherence and anomalous diffusion
- The Exclusion Process: A paradigm for non-equilibrium behaviour
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Operator entanglement entropy of the time evolution operator in chaotic systems
- Anomalous momentum diffusion in a dissipative many-body system
- Rényi generalization of the operational entanglement entropy
- Influence of dephasing on many-body localization
- Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
- Efficient classical simulation of noisy random quantum circuits in one dimension
- Emergence of glass-like dynamics for dissipative and strongly interacting bosons
- Dephasing-induced diffusive transport in anisotropic Heisenberg model
- Operationally accessible entanglement of one dimensional spinless fermions
- Higher Order Methods for Simulations on Quantum Computers
- Coherent and dissipative dynamics at quantum phase transitions
- Strongly interacting ultracold polar molecules
- Quantum entanglement of unitary operators on bi-partite systems
- Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
- Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
- Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
- A solvable family of driven-dissipative many-body systems
- Large deviations of a tracer in the symmetric exclusion process
- Control of the Bose-Einstein condensate by dissipation. Nonlinear Zeno effect
- Dissipative quasi-particle picture for quadratic Markovian open quantum systems
- Dynamics of condensation in the symmetric inclusion process
- Transport in quantum chains under strong monitoring
- Hydrodynamics of quantum entropies in Ising chains with linear dissipation
- Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
- Dynamical universality classes towards an infinite temperature state
- Barrier from chaos: operator entanglement dynamics of the reduced density matrix
- Interplay between coherent and dissipative dynamics of bosonic doublons in an optical lattice
- Laser noise imposed limitations of ensemble quantum metrology