Dynamics of the sub-Ohmic spin-boson model: A comparison of three numerical approaches

Yao, Yao; Duan, Liwei; Lü, Zhiguo; Wu, Chenming; Zhao, Yue

doi:10.1103/physreve.88.023303

Cited by 38 publications

(78 citation statements)

References 78 publications

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“…The form in Eq. (7) is that of a modified spin-boson Hamiltonian; the spin-boson model is one of the most utilized and investigated descriptions of open quantum system behavior [43][44][45][46][47][48]. While not exactly solvable (except in special cases) it contains information about the interplay between a two-level "spin" system and a harmonic bath.…”

Section: Modelmentioning

confidence: 99%

Coherent exciton dynamics in a dissipative environment maintained by an off-resonant vibrational mode

2016

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The interplay between an open quantum system and its environment can lead to both coherent and incoherent behavior. We explore the extent to which strong coupling to a single bosonic mode can alter the coherence properties of a two-level system in a structured environment. This mode is treated exactly, with the rest of the environment comprising a Markovian bath of bosonic modes. The strength of the coupling between the two-level system and the single mode is varied for a variety of forms for the bath spectral density in order to assess whether the coherent dynamics of the two-level system are modified. We find a clear renormalization of the site population oscillation frequency that causes an altered interaction with the bath. This leads to enhanced or reduced coherent behavior of the two-level system, depending on the form of the spectral density function. We present an intuitive interpretation, based on an analytical model, to explain the behavior.

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Section: Modelmentioning

confidence: 99%

Coherent exciton dynamics in a dissipative environment maintained by an off-resonant vibrational mode

2016

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“…It is known that the Davydov single D 1 Ansatz performs well in the strong and intermediate coupling regimes [3]. It may be less accurate in the weak coupling regime.…”

Section: Accuracy Of the Multi-d1 Ansatzmentioning

confidence: 99%

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov D1 states

Wang

Chen

Zhou

et al. 2016

The Journal of Chemical Physics

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Dynamics of the sub-Ohmic spin-boson model is investigated by employing a multitude of the Davydov D1 trial states, also known as the multi-D1 Ansatz. Accuracy in dynamics simulations is improved significantly over the single D1 Ansatz, especially in the weak system-bath coupling regime. The reliability of the multi-D1 Ansatz for various coupling strengths and initial conditions are also systematically examined, with results compared closely with those of the hierarchy equations of motion and the path integral Monte Carlo approaches. In addition, a coherent-incoherent phase crossover in the nonequilibrium dynamics is studied through the multi-D1 Ansatz. The phase diagram is obtained with a critical point sc = 0.4. For sc < s < 1, the coherent-to-incoherent crossover occurs at a certain coupling strength, while the coherent state recurs at a much larger coupling strength. For s < sc, only the coherent phase exists.

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“…Starting down this same route, we study quantum dynamics here only at the simplest Silbey-Harris level, thus using a single variational coherent state as a lowest order approximation for the time-dependent problem (this is also called the Davidov ansatz). Such an approach has been previously applied to study quantum dynamics for a variety of physical problems [31][32][33][34][35], and it can be adapted to address scattering of Fock states [36]. The present study allows us to thoroughly assess the merits and drawbacks of this very economical approach; the numerically-exact full generalization of the systematic CSE to the time domain will be addressed in subsequent work.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

2016

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We investigate the quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the photonic states generated in the waveguide. The model treated consists simply of a two-level system coupled to a bosonic bath (the ohmic spin-boson model). Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines in a single framework ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using Numerical Renormalization Group (NRG) calculations. NRG provides a benchmark for any linear response property throughout the ultra-strong coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide quantum electrodynamics (QED). Finally, the scattering results using the coherent state wavefunction approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.

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Dynamics of the sub-Ohmic spin-boson model: A comparison of three numerical approaches

Cited by 38 publications

References 78 publications

Coherent exciton dynamics in a dissipative environment maintained by an off-resonant vibrational mode

Coherent exciton dynamics in a dissipative environment maintained by an off-resonant vibrational mode

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov D1 states

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

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