Influence functional of many-body systems: temporal entanglement and matrix-product state representation
arXiv:2103.13741 · doi:10.1016/j.aop.2021.168552
Abstract
Feynman-Vernon influence functional (IF) was originally introduced to describe the effect of a quantum environment on the dynamics of an open quantum system. We apply the IF approach to describe quantum many-body dynamics in isolated spin systems, viewing the system as an environment for its local subsystems. While the IF can be computed exactly only in certain many-body models, it generally satisfies a self-consistency equation, provided the system, or an ensemble of systems, are translationally invariant. We view the IF as a fictitious wavefunction in the temporal domain, and approximate it using matrix-product states (MPS). This approach is efficient provided the temporal entanglement of the IF is sufficiently low. We illustrate the versatility of the IF approach by analyzing several models that exhibit a range of dynamical behaviors, from thermalizing to many-body localized. In particular, we study the non-equilibrium dynamics in the quantum Ising model in both Floquet and Hamiltonian settings. We find that temporal entanglement entropy may be significantly lower compared to the spatial entanglement and analyze the IF in the continuous-time limit. We simulate the thermodynamic-limit evolution of local observables in various regimes, including the relaxation of impurities embedded in an infinite-temperature chain, and the long-lived oscillatory dynamics of the magnetization associated with the confinement of excitations. By incorporating disorder-averaging into the formalism, we analyze discrete time-crystalline response using the IF method. In this case, we find that the temporal entanglement entropy scales logarithmically with evolution time. The IF approach offers a new lens on many-body non-equilibrium phenomena, both in ergodic and non-ergodic regimes, connecting the theory of open quantum systems theory to quantum statistical physics.
arXiv comment13 pages, 7 figures, submitted to a special issue of Annals of Physics in honour of P. W. Anderson
References in corpus (37)
- Many-Body Physics with Ultracold Gases
- Chaos and Quantum Thermalization
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Many-body localization, thermalization, and entanglement
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Non-Markovian dynamics in open quantum systems
- Floquet Time Crystals
- Time-evolution methods for matrix-product states
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Many-body localization: an introduction and selected topics
- Many-body localization in periodically driven systems
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Fate of many-body localization under periodic driving
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Strong and weak thermalization of infinite non-integrable quantum systems
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- Real time confinement following a quantum quench to a non-integrable model
- Periodically Driving a Many-Body Localized Quantum System
- Minimally Entangled Typical Thermal State Algorithms
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Exact dynamics in dual-unitary quantum circuits
- Matrix Product States for dynamical simulation of infinite chains
- A theory of many-body localization in periodically driven systems
- Many-body delocalization as a quantum avalanche
- Nonthermal states arising from confinement in one and two dimensions
- Analytically solvable renormalization group for the many-body localization transition
- Quasilocalized dynamics from confinement of quantum excitations
- Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
- Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
- Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
- Scaling Theory of Entanglement at the Many-Body Localization Transition
- Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
- Suppression of transport in non-disordered quantum spin chains due to confined excitations
- Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
- Connecting Entanglement in Time and Space: Improving the Folding Algorithm
- Localization with random time-periodic quantum circuits