Artifact of phonon-induced localization by the existing variational calculations used in the spin-boson model

Chen, Zhide; Wong, Hang

doi:10.1103/physrevb.78.064308

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…That a given solution exists does not necessarily mean that it is appropriate to assume that the system will adopt this value. Rather, we assume that (within our approximate treatment) the system will adopt the value of ∆ r that gives the lowest A B [44]. To see which solution for ∆ r will be favored, we compute the free energy at zero temperature using the variational parameters we have just derived in Eq.…”

Section: B Free Energy Minimizationmentioning

confidence: 99%

“…We conclude this section with a brief summary. For distantly separated spins or negligible Ising strengths, the delocalized-localized crossover corresponds to the well studied single spin-boson model [4,7,38,44]. The critical coupling strength after which the tunneling element is renormalised to zero is predicted to be α c = 1, for ∆/ω c ≪ 1.…”

Section: Section Summarymentioning

confidence: 99%

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Separation-dependent localization in a two-impurity spin-boson model

et al. 2010

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Using a variational approach we investigate the delocalized to localized crossover in the ground state of an Ohmic two-impurity spin-boson model, describing two otherwise non-interacting spins coupled to a common bosonic environment. We show that a competition between an environment-induced Ising spin interaction and externally applied fields leads to variations in the system-bath coupling strength, $\alpha_c$, at which the delocalized-localized crossover occurs. Specifically, the crossover regime lies between $\alpha_c=0.5$ and $\alpha_c=1$ depending upon the spin separation and the strength of the transverse tunneling field. This is in contrast to the analogous single spin case, for which the crossover occurs (in the scaling limit) at fixed $\alpha_c\approx1$. We also discuss links between the two-impurity spin-boson model and a dissipative two-spin transverse Ising model, showing that the latter possesses the same qualitative features as the Ising strength is varied. Finally, we show that signatures of the crossover may be observed in single impurity observables, as well as in the behaviour of the system-environment entanglement.Comment: 12 pages, 9 figures. Published version. Expanded discussion of the distance dependence between the impurities, and added a related figur

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Section: B Free Energy Minimizationmentioning

confidence: 99%

Section: Section Summarymentioning

confidence: 99%

Separation-dependent localization in a two-impurity spin-boson model

et al. 2010

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“…, it also has severe defects, such as spurious transitions [23,[25][26][27][28] and a drastic underestimation of the qubit coherence σ x . Further works aiming at refining the variational Ansatz focused on the simple single-mode case [29][30][31], or were restricted to a non fully-optimal variational state [32].…”

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confidence: 99%

Stabilizing spin coherence through environmental entanglement in strongly dissipative quantum systems

et al. 2014

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The key feature of a quantum spin coupled to a harmonic bath-a model dissipative quantum system-is competition between oscillator potential energy and spin tunneling rate. We show that these opposing tendencies cause environmental entanglement through superpositions of adiabatic and antiadiabatic oscillator states, which then stabilizes the spin coherence against strong dissipation. This insight motivates a fast-converging variational coherent-state expansion for the many-body ground state of the spin-boson model, which we substantiate via numerical quantum tomography.arXiv:1307.5681v2 [quant-ph]

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“…18 However, the variational calculation fails to trace the phonon-induced localization in the strong coupling regime. 19 Now we turn to see the temperature effect on tunneling splitting. Temperature dependence on the dressing factor for the single-mode system is calculated by Eq.…”

Section: Temperature Effect On Quantum Tunnelingmentioning

confidence: 99%

“…The study on this model has a long history and it still attracts a great deal of interest. 1− 19 The basic question is how thermal fluctuations from the environment influence quantum tunneling of the TSS since all the real systems are at finite temperature. The answer to this question is important for the observation of macroscopic quantum phenomena and also for the realization of the quantum computer where the stability of a "qubit" against thermal fluctuations is critical.…”

Section: Introductionmentioning

confidence: 99%

The temperature influence on quantum tunneling in the spin-boson model

Chen,

Huang,

Wong

2008

Preprint

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The existing studies of the temperature effect of the spin-boson model show that the tunneling splitting will increase with temperature, no matter how weak the couplings are between the bath and the spin. However, the small polaron theory said that in the weak coupling and low temperature regime, the tunneling is, in fact, dominated by the diagonal transitions whereas this diagonal contribution to the tunneling should be faded away with increasing temperature. Taking advantage of the analysis originated from the Feynman-Vernon's influence functional theory, the influence on the tunneling by the phonon bath can be expressed as a product of the effects of every single phonon mode, which can be studied by numerical exact diagonalization. We find that, in the weak coupling and low temperature regime, all the spin-single-mode systems exhibit the same decreasing dependence of tunneling on increasing temperature. In turn, with the conclusion of influence functional theory, the tunneling of the spin-boson model should decrease and it is independent of the bath structure. In the strong coupling regime, however, the temperature effect reverses from suppressing to enhancing the tunneling with the increase of temperature. Discrepancies between the old theories and the small polaron theory are also explained.

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Artifact of phonon-induced localization by the existing variational calculations used in the spin-boson model

Cited by 6 publications

References 28 publications

Separation-dependent localization in a two-impurity spin-boson model

Separation-dependent localization in a two-impurity spin-boson model

Stabilizing spin coherence through environmental entanglement in strongly dissipative quantum systems

The temperature influence on quantum tunneling in the spin-boson model

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