Generalized numerical renormalization group for dynamical quantities

Area of Science:

• Condensed matter physics
• Quantum many-body systems
• Computational physics

Background:

• The numerical renormalization group (NRG) is a powerful tool for studying strongly correlated electron systems.
• Calculating dynamical properties in NRG can be challenging, particularly when energy scales are not well separated.
• The Anderson impurity model is a fundamental model in condensed matter physics, often studied using NRG.

Purpose of the Study:

• To introduce a novel approach for computing dynamical properties within the numerical renormalization group (NRG).
• To address the failure of existing NRG methods for the Anderson impurity in a magnetic field, caused by a lack of energy scale separation.
• To provide a unified framework for calculating dynamics across all temperatures.

Main Methods:

• Developing a new NRG approach for dynamical property calculations.
• Evaluating the Green function using the reduced density matrix of the entire system.
• Comparing results with static magnetization to validate accuracy.

Main Results:

• The new method successfully calculates accurate dynamical spectra for the Anderson impurity model in a magnetic field.
• The results show excellent agreement with static magnetization data.
• The approach overcomes the limitations of previous NRG methods related to energy scale separation.

Conclusions:

• The introduced NRG method provides a robust and accurate way to compute dynamical properties.
• This work offers a correct extension of Wilson's original thermodynamic NRG calculations.
• The new procedure unifies the calculation of dynamics at any temperature, applicable to various strongly correlated systems.