Equilibrium and nonequilibrium dynamics of the sub-Ohmic spin-boson model

Area of Science:

• Quantum physics
• Condensed matter theory
• Quantum information science

Background:

• The spin-boson model describes a two-level system interacting with a bosonic environment.
• Understanding the dynamics of such systems is crucial for quantum technologies, particularly qubits.
• Previous studies often focused on Ohmic damping, limiting applicability to specific noise types.

Purpose of the Study:

• To investigate the dynamics of the spin-boson model with sub-Ohmic spectral density J(omega) proportional to omega(s).
• To characterize the delocalized phase and identify unique features compared to Ohmic damping.
• To explore the possibility of coherent oscillations in the localized phase of the sub-Ohmic model.

Main Methods:

• Utilized the nonperturbative numerical renormalization group (NRG) method for accurate simulations.
• Analyzed the system's behavior across different regimes of the spectral density exponent 's'.
• Focused on short and long time-scale dynamics and energy scale characterization.

Main Results:

• The delocalized phase in the sub-Ohmic model is not characterized by a single energy scale, indicating a nontrivial quantum phase transition.
• In the strongly sub-Ohmic regime (s<<1), weakly damped coherent oscillations are observed on short timescales, even within the localized phase.
• This contrasts with the behavior typically seen in systems with Ohmic damping.

Conclusions:

• The sub-Ohmic spin-boson model presents richer and more complex dynamics than previously understood.
• The presence of short-time coherent oscillations in the localized phase has significant implications for the design and stability of quantum bits (qubits) exposed to electromagnetic noise.
• Further research into non-Ohmic damping regimes is essential for advancing quantum technologies.