Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model

TL;DR

This paper extends Wilson's Numerical Renormalization Group method to bosonic impurity models, enabling non-perturbative analysis of quantum phase transitions in the spin-boson model with subohmic baths.

Contribution

It introduces a generalized NRG approach for bosonic systems and applies it to reveal quantum phase transitions in the spin-boson model.

Findings

Identified a line of continuous quantum phase transitions for 0<s<1

Confirmed the Kosterlitz-Thouless transition at s=1

Connected results with perturbative renormalization group studies

Abstract

We describe the generalization of Wilson's Numerical Renormalization Group method to quantum impurity models with a bosonic bath, providing a general non-perturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) ~ omega^s. We find clear evidence for a line of continuous quantum phase transitions for subohmic bath exponents 0<s<1; the line terminates in the well-known Kosterlitz-Thouless transition at s=1. Contact is made with results from perturbative renormalization group, and various other applications are outlined.