Quantum phase transitions in a resonant-level model with dissipation: Renormalization-group studies

TL;DR

This paper investigates quantum phase transitions in a dissipative resonant-level model with power-law hybridization and bosonic bath spectra, using renormalization-group methods to map out the phase diagram and critical behavior.

Contribution

It provides a comprehensive analysis of the phase diagram and critical properties of a Bose-Fermi quantum impurity model with general spectral functions, extending understanding of dissipation effects.

Findings

Identifies a continuous transition between delocalized and localized phases.

Shows phase diagram depends on power-law exponents of hybridization and bosonic bath.

Finds critical properties match those of known models for specific parameters.

Abstract

We study a spinless level that hybridizes with a fermionic band and is also coupled via its charge to a dissipative bosonic bath. We consider the general case of a power-law hybridization function $\Gamma(\w)\propto |\w|^r$ with $r\ge 0$, and a bosonic bath spectral function $B(\w)\propto \w^s$ with $s\ge -1$. For $r<1$ and $\mathrm{max}(0,2r-1)<s<1$, this Bose-Fermi quantum impurity model features a continuous zero-temperature transition between a delocalized phase, with tunneling between the impurity level and the band, and a localized phase, in which dissipation suppresses tunneling in the low-energy limit. The phase diagram and the critical behavior of the model are elucidated using perturbative and numerical renormalization-group techniques, between which there is excellent agreement in the appropriate regimes. For $r=0$ this model's critical properties coincide with those of the spin-boson and Ising Bose-Fermi Kondo models, as expected from bosonization.