Quantum criticality of the sub-Ohmic spin-boson model

Kirchner, Stefan; Ingersent, Kevin; Si, Qimiao

doi:10.1103/physrevb.85.075113

Cited by 17 publications

(10 citation statements)

References 26 publications

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“…This is due to the development of a localized, so-called "trapped", state for the pseudospin (in a double-well analogy). The phase transition point to the trapped state, η c = η c (n), depends on the power law of the spectral density [30][31][32][33] . Despite the potential occurence of a phase transition, the perturbative approach can be applied for the shorttime dynamics 31,32 , which in view of the limited coherence times of, in particular, flux qubits will generally suffice.…”

Section: Fig 2 Decoherence Time Ratio Tmentioning

confidence: 99%

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily smallT2/T1decoherence time ratios

Noh

Fischer

2014

Phys. Rev. B

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We present a perturbative treatment of the subohmic spin-boson model which remedies a crucial flaw in previous treatments. The problem is traced back to the incorrect application of a Markov type approximation to specific terms in the temporal evolution of the reduced density matrix. The modified solution is consistent both with numerical simulations and the exact solution obtained when the bath-coupling spin-space direction is parallel to the qubit energy-basis spin. We therefore demonstrate that the subohmic spin-boson model is capable of describing arbitrarily small ratios of the T2 and T1 decoherence times, associated to the decay of the off-diagonal and diagonal reduced density-matrix elements, respectively. An analytical formula for T2/T1 at the absolute zero of temperature is provided in the limit of a subohmic bath with vanishing spectral power law exponent. Small ratios closely mimic the experimental results for solid state (flux) qubits, which are subject predominantly to low-frequency electromagnetic noise, and we suggest a reanalysis of the corresponding experimental data in terms of a nonanalytic decay of off-diagonal coherence.Since the advent of quantum information technology, the problem of two-state systems aka qubits, immersed in environmental (bath) degrees of freedom has increasingly gained importance, cf., e.g., 1-3 . The spin-boson model, succinctly describing such a physical situation, namely an open two-state quantum system interacting with a bath, accounts for two-state energy relaxation and dephasing, and therefore has been studied extensively 4,5 . It was, for example, used to describe physical contexts as diverse as flux qubits implemented using superconducting quantum interference devices (SQUIDs) 6-10 , electron transfer in biomolecules 11 , and phonon coupling in atomic tunneling 12 . The spin-boson model introduces a continuum of independent simple harmonic oscillators with a given spectral weight distribution as the environment, assuming them to couple with the qubit linearly. The Hamiltonian of the entire (closed) system therefore reads (setting = 1)Here, − → σ = (σ x , σ y , σ z ) are the usual Pauli matrices andb † k ,b k are creation and annihilation operators of harmonic oscillators in the (infinitely extended) bath, labelled by the quantum number(s) k, which can stand, e.g., for the momentum of the bath excitations. The coupling direction − → n is parametrized by two angles θ,ϕ as − → n = (sin θ cos ϕ, sin θ sin ϕ, cos θ).The bath is conventionally characterized by the quantity J(ω) ≡ k λ 2 k δ(ω − ω k ), which determines the dynamics of the spin-boson model. This spectral density of the bath is effectively a density of states summation weighed by the coupling strength squared λ 2 k , hence the name. Usually it is assumed that J(ω) is of a power law form up to a cutoff, J(ω) = ηω, where ω c is the (physical) cutoff frequency of the bath, assumed to be much larger than the system frequency spacing ω s . The strength of coupling is parametrized by the dimensionless η. Baths h...

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Section: Fig 2 Decoherence Time Ratio Tmentioning

confidence: 99%

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily smallT2/T1decoherence time ratios

Noh

Fischer

2014

Phys. Rev. B

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“…So far, the quantum-to-classical mapping has been confirmed in the range 0 < s < 1/2 by studying behaviors of the critical exponent ν and the dynamical exponent z [49]. However, in the sub-Ohmic regime with 1/2 < s < 1, no consensus has reached [13,30,31,32,33,34,52,53].…”

Section: Sub-ohmic Dissipationmentioning

confidence: 99%

Green’s functions for spin boson systems: Beyond conventional perturbation theories

Liu

2016

Chemical Physics

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Unraveling general properties of Green's functions of quantum dissipative systems is of both experimental relevance and theoretical interest. Here, we study the spin-boson model as a prototype. By utilizing the Majorana-Fermion representation together with the polaron transformation, we establish a theoretical approach to analyze Green's functions of the spin-boson model. In contrast to conventional perturbation theories either in the tunneling energy or in the system-bath coupling strength, the proposed scheme gives reliable results over wide regimes of the coupling strength, bias, as well as temperature. To demonstrate the utility of the approach, we consider the susceptibility as well as the symmetrized spin correlation function (SSCF) which can be expressed in terms of Green's functions. Thorough investigations are made on systems embedded in Ohmic or sub-Ohmic bosonic baths. We found the so-obtained SSCF is the same as that of the non-interacting blip approximation (NIBA) in unbiased systems while it is applicable for a wider range of temperature in the biased systems compared with the NIBA. We also show that a previous perturbation result is recovered as a weak coupling limit of the so-obtained SSCF. Furthermore, by studying the quantum criticality of the susceptibility, we confirm the validity of the quantum-toclassical mapping in the whole sub-Ohmic regime.

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“…The numerical renormalization group (NRG) is well established for fermionic systems [3][4][5]. In the last decade the NRG has been extended to bosonic environments [9,10,60,74,75] and lately combined for Bose-Fermi impurity systems [14,15,18]. We shortly summarize the NRG procedure [15] for an environment consisting of bosonic as well as fermionic DOFs.…”

Section: B the Numerical Renormalization Group Formentioning

confidence: 99%

Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

Kleine¹,

Anders²

2015

Preprint

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We investigate the influence of an additional bosonic bath onto the real-time dynamics of a localized orbital coupled to conduction band with an energy-dependent coupling function Γ(ε) ∝ |ε| r . Recently, a rich phase diagram has been found in this Bose-Fermi Anderson model, where the transitions between competing ground states are governed by quantum critical points. In addition to a transition between a Kondo singlet and a local moment, a localized phase has been established once the coupling to a sub-ohmic bosonic bath exceeds a critical value. Using the time-dependent numerical renormalization group approach, we show that the non-equilibrium dynamics with Ftype of bath exponents can be fully understand within an effective single-impurity Anderson model using a renormalized local Coulomb interaction Uren. For regimes with B-type of bath exponents, the nature of the bosonic bath and the coupling strength has a profound impact on the electron dynamics which can only partially be understood using an appropriate Uren. The local expectation values always reach a steady state at very long times. By a scaling analysis for Λ → 1 + , we find thermalization of the system only in the strong coupling regime. In the local moment and in the localized phase significant deviations between the steady-state value and the thermal equilibrium value are found that are related to the distance to the quantum critical point.

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Quantum criticality of the sub-Ohmic spin-boson model

Cited by 17 publications

References 26 publications

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily smallT2/T1decoherence time ratios

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily smallT2/T1decoherence time ratios

Green’s functions for spin boson systems: Beyond conventional perturbation theories

Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

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