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arXiv:2101.09463 · Physical Review A

Non-Markovian effects in the spin-boson model at zero temperature

Sebastian Wenderoth, Heinz‐Peter Breuer, Michael Thoss

Published Jul 19, 2021• 26 citations
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Abstract

We investigate memory effects in the spin-boson model using a recently proposed measure for non-Markovian behavior based on the information exchange between an open system and its environment. Employing the numerical exact multilayer multiconfiguration time-dependent Hartree approach, we simulate the dynamics of the spin-boson model at zero temperature for a broad range of parameters. For a fast bath, i.e., in the scaling limit, we find non-Markovian dynamics for a coherently decaying spin at weak system-bath coupling, whereas memory effects are absent for stronger coupling in the regimes of incoherent decay and localization. If the timescales of system and bath are comparable, a complex, nonmonotonic dependence of non-Markovianity on the system-bath coupling strength is observed.

DOI
10.1103/physreva.104.012213

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•Sep 14, 2017•15 citations
We investigate memory effects in the spin-boson model using a recently proposed measure for non-Markovian behavior based on the information exchange between an open system and its environment. Employing the numerical exact multilayer multiconfiguration time-dependent Hartree approach, we simulate the dynamics of the spin-boson model at zero temperature for a broad range of parameters. For a fast bath, i.e., in the scaling limit, we find non-Markovian dynamics for a coherently decaying spin at weak system-bath coupling, whereas memory effects are absent for stronger coupling in the regimes of incoherent decay and localization. If the timescales of system and bath are comparable, a complex, nonmonotonic dependence of non-Markovianity on the system-bath coupling strength is observed.
The dynamics of the spin-boson model at zero temperature is investigated using the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method.This method allows a numerically exact description of the dynamics of the spin-boson model in a broad range of coupling strengths.The results show the transition of the dynamics from weakly damped coherent motion to incoherent decay and finally to localization upon increase of the system-bath coupling strength.A detailed analysis of the incoherent decay for stronger coupling reveals that multiple timescales are involved in the dynamics.Furthermore, the applicability of the scaling limit for large characteristic frequencies of the bath as well as the validity of the non-interacting blip approximation are studied in some detail.
Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master equation without the Markov or rotating wave approximations. While the dynamics is found to be strongly non-Markovian for low temperatures and cutoffs, in general, we observe a special regime favoring Markovian behavior. This effect is explained as resulting from a resonance between the system's transition frequency and the frequencies of the dominant environmental modes. We further demonstrate that the corresponding Redfield equation is capable of reproducing the characteristic features of the non-Markovian quantum behavior of the model.
We investigate the nature of memory effects in the non-Markovian dynamics of spin-boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We focus on two such criteria, one based on the dynamical map and the other on single-intervention process tensors, and discuss their connection. We apply these criteria to quench dynamics in spin-boson and two-spin-boson models, computed using a numerically exact method for non-Markovian open-system dynamics based on matrix product operator influence functionals. This method is ideally suited to simulate quantum multitime processes in spin-boson models across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, it is still possible to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.
Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.