Quantum phase transitions in a pseudogap Anderson-Holstein model

TL;DR

This paper investigates quantum phase transitions in a pseudogap Anderson-Holstein model, revealing how impurity-boson coupling influences the transition types and universality classes, with potential experimental realization in quantum-dot devices.

Contribution

It introduces a detailed analysis of quantum phase transitions in a pseudogap Anderson-Holstein model, highlighting the effects of impurity-boson coupling and spin-charge symmetry on critical behavior.

Findings

Quantum phase transitions depend on impurity-boson coupling strength.

Transitions include Kondo, local-moment, charge-Kondo, and local-charge phases.

Critical exponents are universal and relate to the pseudogap Anderson model.

Abstract

We study a pseudogap Anderson-Holstein model of a magnetic impurity level that hybridizes with a conduction band whose density of states vanishes in power-law fashion at the Fermi energy, and couples, via its charge, to a nondispersive bosonic mode (e.g., an optical phonon). The model, which we treat using poor-man's scaling and the numerical renormalization group, exhibits quantum phase transitions of different types depending on the strength of the impurity-boson coupling. For weak impurity-boson coupling, the suppression of the density of states near the Fermi energy leads to quantum phase transitions between strong-coupling (Kondo) and local-moment phases. For sufficiently strong impurity-boson coupling, however, the bare repulsion between a pair of electrons in the impurity level becomes an effective attraction, leading to quantum phase transitions between strong-coupling (charge-Kondo) and local-charge phases. Even though the Hamiltonian exhibits different symmetries in the spin and charge sectors, the thermodynamic properties near the two types of quantum phase transition are closely related under spin-charge interchange. Moreover, the critical responses to a local magnetic field (for small impurity-boson coupling) and to an electric potential (for large impurity-boson coupling) are characterized by the same exponents, whose values place these quantum critical points in the universality class of the pseudogap Anderson model. One specific case of the pseudogap Anderson-Holstein model may be realized in a double-quantum-dot device, where the quantum phase transitions manifest themselves in the finite-temperature linear electrical conductance.