Learning the non-Markovian features of subsystem dynamics
arXiv:2507.14133 · doi:10.21468/SciPostPhys.19.6.149
Abstract
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.
25 pages, 11 figures
References in corpus (47)
- Nonequilibrium dynamics of closed interacting quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Non-Markovian dynamics in open quantum systems
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum trajectories and open many-body quantum systems
- Open Quantum Systems. An Introduction
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Canonical form of master equations and characterization of non-Markovianity
- On measures of non-Markovianity: divisibility vs. backflow of information
- Geometrical characterization of non-Markovianity
- Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
- Matrix Product States for dynamical simulation of infinite chains
- Optimal state pairs for non-Markovian quantum dynamics
- Finding the Kraus decomposition from a master equation and vice versa
- Witness for initial system-environment correlations in open system dynamics
- Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Completely Positive Divisibility Does Not Mean Markovianity
- Quantum dynamics of thermalizing systems
- Generalized trace distance measure connecting quantum and classical non-Markovianity
- Influence matrix approach to many-body Floquet dynamics
- Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
- Temporal entanglement, quasiparticles and the role of interactions
- Connecting Entanglement in Time and Space: Improving the Folding Algorithm
- Non-unital non-Markovianity of quantum dynamics
- Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
- Constructing Tensor Network Influence Functionals for General Quantum Dynamics
- The Lyapunov Spectrum of Quantum Thermalisation
- Almost Markovian processes from closed dynamics
- Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
- Light cone tensor network and time evolution
- Time-evolution of local information: thermalization dynamics of local observables
- Machine learning time-local generators of open quantum dynamics
- On temporal entropy and the complexity of computing the expectation value of local operators after a quench
- From observations to complexity of quantum states via unsupervised learning
- Converting long-range entanglement into mixture: tensor-network approach to local equilibration
- Exact Hidden Markovian Dynamics in Quantum Circuits
- Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
- Inferring interpretable dynamical generators of local quantum observables from projective measurements through machine learning
- Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
- Universal Characterization of Quantum Many-Body States through Local Information
- Machine learning of quantum channels on NISQ devices
- Non-Markovianity of subsystem dynamics in isolated quantum many-body systems
- Overcoming the entanglement barrier with sampled tensor networks
- Density matrices in quantum field theory: Non-Markovianity, path integrals and master equations