Numerical Renormalization Group for Quantum Impurities in a Bosonic Bath

TL;DR

This paper details a numerical renormalization group method for quantum impurity models coupled to bosonic baths, demonstrating high accuracy across various parameters and temperatures, and applying it to the spin-boson model.

Contribution

It introduces a comprehensive NRG approach for bosonic baths, including implementation details and validation against exact and existing numerical results.

Findings

Accurate results for static and dynamic quantities

Effective discretization of bosonic spectral density

Convergence demonstrated across parameters and temperatures

Abstract

We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and sub-Ohmic cases. We present various results for static as well as dynamic quantities and discuss details of the numerical implementation, e.g., the discretization of a bosonic bath with arbitrary continuous spectral density, the suitable choice of a finite basis in the bosonic Hilbert space, and questions of convergence w.r.t. truncation parameters. The method is shown to provide high-accuracy data over the whole range of model parameters and temperatures, which are in agreement with exact results and other numerical data from the literature.