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

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(omega)proportional to vertical bar omega(r)vertical bar, with r >= 0, and a bosonic-bath spectral function B(omega)proportional to omega(s), with s >=-1. For r < 1 and 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.