TY - JOUR
T1 - Influence functional of many-body systems
T2 - Temporal entanglement and matrix-product state representation
AU - Sonner, Michael
AU - Lerose, Alessio
AU - Abanin, Dmitry A.
N1 - Funding Information:
This work was supported by the Swiss National Science Foundation and by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 864597). We thank Lorenzo Piroli and Soonwon Choi for useful discussions. Computations were performed at the University of Geneva on the “Baobab” and “Yggdrasil” HPC clusters. The datasets generated and analyzed during the current study are available at 10.26037/yareta:n2rcvndqg5dvfk3v42qiqoqf34 and will be preserved for 10 years. All Authors have contributed significantly to presented research, by performing analytical and numerical calculations, interpreting them, and writing the manuscript.
Funding Information:
This work was supported by the Swiss National Science Foundation and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 864597 ). We thank Lorenzo Piroli and Soonwon Choi for useful discussions. Computations were performed at the University of Geneva on the “Baobab” and “Yggdrasil” HPC clusters. The datasets generated and analyzed during the current study are available at 10.26037/yareta:n2rcvndqg5dvfk3v42qiqoqf34 and will be preserved for 10 years. All Authors have contributed significantly to presented research, by performing analytical and numerical calculations, interpreting them, and writing the manuscript.
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/8
Y1 - 2021/8
N2 - 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 broad applicability 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. Furthermore, by incorporating disorder-averaging into the formalism, we analyze discrete time-crystalline response using the IF of a bond-disordered kicked Ising chain. 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 to quantum statistical physics.
AB - 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 broad applicability 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. Furthermore, by incorporating disorder-averaging into the formalism, we analyze discrete time-crystalline response using the IF of a bond-disordered kicked Ising chain. 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 to quantum statistical physics.
KW - Many-body localization
KW - Open quantum systems
KW - Periodically driven (Floquet) many-body systems
KW - Quantum many-body dynamics
KW - Thermalization
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U2 - 10.1016/j.aop.2021.168552
DO - 10.1016/j.aop.2021.168552
M3 - Article
AN - SCOPUS:85108979588
SN - 0003-4916
VL - 431
JO - Annals of Physics
JF - Annals of Physics
M1 - 168552
ER -