Single-particle dynamics of the Anderson model: a two-self-energy description within the numerical renormalization group approach

Single-particle dynamics of the Anderson impurity model are studied using both the numerical renormalization group (NRG) method and the local moment approach (LMA). It is shown that a 'two-self-energy' description of dynamics inherent to the LMA, as well as a conventional 'single-self-energy' description, arise within NRG; each yielding correctly the same local single-particle spectrum. Explicit NRG results are obtained for the broken symmetry spectral constituents arising in a two-self-energy description, and the total spectrum. These are also compared to analytical results obtained from the LMA as implemented in practice. Very good agreement between the two is found, essentially on all relevant energy scales from the high-energy Hubbard satellites to the low-energy Kondo resonance.Comment: 12 pages, 6 figure

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.Comment: 14 pages, 6 figure

Spectral scaling and quantum critical behaviour in the pseudogap Anderson model

The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid and local moment phases, via the local moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi liquid, interacting nature of the fixed point.Comment: 7 pages, 2 figure

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations

Interview with Scott and Carrie Logan by Mike Hastings

Biographical NoteScott Logan was born on February 17, 1977, in Exeter, New Hampshire. His father, Terence Logan, held a Ph.D. from Harvard University and taught English at the University of New Hampshire. Scott’s mother was from rural southern Maryland, and they met at Newton College of the Sacred Heart, in Newton, Massachusetts, where Terence was a professor and Scott’s mother was a student. Scott grew up in Kennebunk, Maine, and was interested in collecting and selling antiques, and in local history. For this business, he received a scholarship from the National Association of the Self-Employed. He was also one of the first Mitchell Scholars, in 1995, attending Bowdoin College and graduating in 1999. He first met his future wife, Carrie, at Bowdoin through their mutual membership in Alpha Delta Phi fraternity. He worked at Christie’s Auction Company and then the auctioneering firm Skinner, Inc. He then attended law school at Boston College, and at the time of this interview, he was an attorney specializing in consumer bankruptcy. Carrie Logan was born on December 24, 1977, in Portland, Maine, to Donald McGilvery and Cheryl Poulin McGilvery. Her parents, both from Maine, met at Cony High School, and both were graduated from the University of Maine, Orono. Her father worked in architecture and construction management for the Maine State Housing Authority, and her mother worked in education and at the time of this interview was the secretary at William H. Rowe School in Yarmouth. Carrie grew up in Yarmouth, Maine, attended Yarmouth public schools, and was selected as a Mitchell Scholar. She attended Bowdoin College, where she met Scott, and was graduated with the class of 2000. Through the Teach For America program, she taught in Opelousas, Louisiana, for two years and then became an English-as-a-Second-Language teacher in Houston, Texas, before returning to Maine to study at the University of Maine School of Law. She took her law degree in 2007 and was practicing business and real estate law at Preti Flaherty in Portland, Maine, at the time of this interview. SummaryInterview includes discussion of: Scott’s family and educational background in Kennebunk; Scott’s antique bottle interest; Scott’s education; Carrie’s family and educational background in Yarmouth; the decision to go to Bowdoin College; paying for college; the Mitchell Institute and Mitchell Scholarship; life at Bowdoin and Alpha Delta Phi; Carrie’s work teaching in the South with Teach for America; coming back to Maine; Scott dealing antiques; and more recent involvement with the Mitchell Institute