Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Theory
• Computational Physics

Background:

• Quantum impurity models are crucial for understanding complex quantum phenomena.
• Bosonic baths introduce unique challenges in theoretical modeling.
• Existing methods often struggle with nonperturbative regimes and low temperatures.

Purpose of the Study:

• To generalize Wilson's numerical renormalization group (NRG) method for quantum impurity models involving bosonic baths.
• To develop a general nonperturbative approach for studying bosonic impurity models.
• To investigate quantum phase transitions in the spin-boson model.

Main Methods:

• Generalization of Wilson's numerical renormalization group (NRG) method.
• Application to quantum impurity models with bosonic baths.
• Analysis of the spin-boson model with a power-law spectral density J(omega) proportional to omega(s).

Main Results:

• The developed NRG method provides access to exponentially small energies and temperatures.
• Clear evidence for a line of continuous quantum phase transitions was found for sub-Ohmic bath exponents (0
• This transition line terminates at the Kosterlitz-Thouless transition point (s=1).

Conclusions:

• The generalized NRG method offers a powerful nonperturbative tool for bosonic impurity models.
• The study elucidates the nature of quantum phase transitions in the spin-boson model.
• The findings establish a connection with perturbative renormalization group results and suggest broad applicability.