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

Area of Science:

• Quantum Mechanics
• Condensed Matter Physics
• Chemical Physics

Background:

• The spin-boson model describes quantum systems interacting with a bath of harmonic oscillators.
• Strong friction and sub-Ohmic spectral densities present challenges for theoretical modeling.
• Understanding quantum dynamics under these conditions is crucial for various physical phenomena.

Purpose of the Study:

• To investigate the dynamics of the zero-temperature sub-Ohmic spin-boson model with strong friction.
• To explore the influence of phonon bath initial conditions on quantum dynamics.
• To assess the validity and robustness of the Dirac-Frenkel time-dependent variational approach with the Davydov D1 ansatz.

Main Methods:

• Employing the Dirac-Frenkel time-dependent variational principle.
• Utilizing the Davydov D1 ansatz for the quantum state.
• Simulating the dynamics under different initial conditions for the phonon bath (polarized vs. factorized).

Main Results:

• Phonon bath initial conditions critically influence the system's dynamics.
• Quantum coherence survives in the strong coupling regime with a polarized bath initial condition.
• Quantum coherence is absent with a factorized bath initial condition.
• A transition from coherent to incoherent dynamics occurs at a critical coupling strength (α ≈ 0.1) for s = 0.25 under the factorized initial condition.

Conclusions:

• The time-dependent variational approach is robust for simulating quantum dynamics in systems with strong dissipation and deep sub-Ohmic baths.
• The choice of initial conditions for the environment is a critical factor in determining the observable quantum effects.
• The Davydov D1 ansatz provides a reliable method for probing these complex quantum phenomena.