Quantum phase transitions in a pseudogap Anderson-Holstein 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.

26 pages and 19 figures

References in corpus (39)

• Correlated Electrons in High Temperature Superconductors
• The numerical renormalization group method for quantum impurity systems
• Quantum Criticality in Heavy Fermion Metals
• Continuous Quantum Phase Transitions
• Bose-Einstein Condensation in Magnetic Insulators
• Heavy Fermions and Quantum Phase Transitions
• Observation of the two-channel Kondo effect
• Quantum phase transition in a single-molecule quantum dot
• Renormalization-group study of Anderson and Kondo impurities in gapless Fermi systems
• Theoretical Studies of Superconductor-Insulator Transitions
• Impurity Quantum Phase Transitions
• Single electron-phonon interaction in a suspended quantum dot phonon cavity
• Anderson impurity in pseudo-gap Fermi systems
• Many Body Effects on the Transport Properties of Single-Molecule Devices
• Quantum Phase Transition in a Multi-Level Dot
• Theory of Current and Shot Noise Spectroscopy in Single-Molecular Quantum Dots with Phonon Mode
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• Numerical Renormalization Group Study of the Anderson-Holstein Impurity Model
• Multi-impurity Anderson model for quantum dots coupled in parallel
• Quantum phase transition in capacitively coupled double quantum dots
• Behavior of magnetic impurities in gapless Fermi systems
• Zero-field Kondo splitting and quantum-critical transition in double quantum dots
• Quantum phase transition in a two-channel-Kondo quantum dot device
• Critical local-moment fluctuations, anomalous exponents, and omega/T scaling in the Kondo problem with a pseudogap
• Quantum transport through a deformable molecular transistor
• Anderson impurities in gapless hosts: comparison of renormalization group and local moment approaches
• Quantum Phase Transitions and Conserved Charges
• Kondo effect of impurity moments in d-wave superconductors: Quantum phase transition and spectral properties
• Mechanism for large thermoelectric power in negative-U molecular quantum dots
• A Local Moment Approach to magnetic impurities in gapless Fermi systems
• Correlated electron physics in multilevel quantum dots: phase transitions, transport, and experiment
• Numerical renormalization group study of the symmetric Anderson-Holstein model: phonon and electron spectral functions
• Tunable pseudogap Kondo effect and quantum phase transitions in Aharonov-Bohm interferometers
• Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory
• Finite-temperature conductance signatures of quantum criticality in double quantum dots
• Local quantum phase transition in the pseudogap Anderson model: scales, scaling and quantum critical dynamics
• Signatures of quantum phase transitions in parallel quantum dots: Crossover from local-moment to underscreened spin-1 Kondo physics
• Slave-boson approach to the infinite-U Anderson-Holstein impurity model
• A path integral approach to Anderson-Holstein model

Cited by in corpus (10)

• Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots
• Gate-tunable Kondo resistivity and dephasing rate in graphene studied by numerical renormalization group calculations
• Critical charge fluctuations in a pseudogap Anderson model
• Nonequilibrium Kondo effect by equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias
• Nonequilibrium Kondo effect in a graphene-coupled quantum dot in the presence of a magnetic field
• Phase boundaries of the pseudogap Anderson and Kondo models
• Reentrant Kondo effect in a quantum impurity coupled to a metal-semiconductor hybrid contact
• Entanglement Entropy Near Kondo-Destruction Quantum Critical Points
• Quantum phase transitions in superconductor--quantum-dot--superconductor Josephson structures with attractive intradot interaction
• Stochastic Schrödinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective