We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength $\ensuremath{\alpha}$ and to exist for any power $0<s<1$ , where the bath coupling is described by $J(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\alpha}{\ensuremath{\omega}}^{s}$. We find nonmonotonic temperature dependence of the two-level gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}$ and a reentrance regime close to the transition due to nonadiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength $\ensuremath{\alpha}$ and to exist for any power $0<s<1$, where the bath coupling is described by $J(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\alpha}{\ensuremath{\omega}}^{s}$. We find nonmonotonic temperature dependence of the two-level gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}$ and a reentrance regime close to the transition due to nonadiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.

arXiv:cond-mat/0511285Physical Review BFeb 7, 200654 citations

Dynamics of the sub-Ohmic spin-boson model: A time-dependent variational study

Ning Wu, Liwei Duan, Xin Li +1 more

The Dirac-Frenkel time-dependent variation is employed to probe the dynamics of the zero temperature sub-Ohmic spin-boson model with strong friction utilizing the Davydov D1 ansatz. It is shown that initial conditions of the phonon bath have considerable influence on the dynamics. Counterintuitively, even in the very strong coupling regime, quantum coherence features still manage to survive under the polarized bath initial condition, while such features are absent under the factorized bath initial condition. In addition, a coherent-incoherent transition is found at a critical coupling strength α ≈ 0.1 for s = 0.25 under the factorized bath initial condition. We quantify how faithfully our ansatz follows the Schrödinger equation, finding that the time-dependent variational approach is robust for strong dissipation and deep sub-Ohmic baths (s ≪ 1).The Dirac-Frenkel time-dependent variation is employed to probe the dynamics of the zero temperature sub-Ohmic spin-boson model with strong friction utilizing the Davydov D1 ansatz. It is shown that initial conditions of the phonon bath have considerable influence on the dynamics. Counterintuitively, even in the very strong coupling regime, quantum coherence features still manage to survive under the polarized bath initial condition, while such features are absent under the factorized bath initial condition. In addition, a coherent-incoherent transition is found at a critical coupling strength α ≈ 0.1 for s = 0.25 under the factorized bath initial condition. We quantify how faithfully our ansatz follows the Schrödinger equation, finding that the time-dependent variational approach is robust for strong dissipation and deep sub-Ohmic baths (s ≪ 1).

arXiv:1302.1682The Journal of Chemical PhysicsFeb 28, 201342 citations

Some results on the spin-boson model

Juan José García‐Ripoll

Aug 20, 20140 citations

0<s<1

, where the bath coupling is described by $J(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\alpha}{\ensuremath{\omega}}^{s}$. We find nonmonotonic temperature dependence of the two-level gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}$ and a reentrance regime close to the transition due to nonadiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.