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We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and sub-Ohmic cases. We present various results for static as well as dynamic quantities and discuss details of the… (More)

- Ralf Bulla, Ning-Hua Tong, Matthias Vojta
- Physical review letters
- 2003

We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to… (More)

We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-1 2 Kondo impurities coupled to a single orbital of the host. We investigate the phase… (More)

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group ͑NRG͒ method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG… (More)

- R. Bulla
- 1999

The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle… (More)

- Th. Pruschke, R. Bulla, M. Jarrell
- 2000

Wilson's numerical renormalization-group method is used to study the paramagnetic ground state of the periodic Anderson model within the dynamical mean-field approach. For the particle-hole symmetric model, which is a Kondo insulator, we find that the lattice Kondo scale T 0 is strongly enhanced over the impurity scale T K ; T 0 /T K ϰexp͕1/3I͖, where I is… (More)

- Ralf Bulla
- 2000

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This… (More)

In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renor-malization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin.… (More)

- T Hecht, A Weichselbaum, J von Delft, R Bulla
- Journal of physics. Condensed matter : an…
- 2008

We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows that, contrary to previous belief, NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the… (More)

- J. Martinek, M. Sindel, +5 authors S. Maekawa
- 2005

The effect of a gate voltage ͑V g ͒ on the spin splitting of an electronic level in a quantum dot ͑QD͒ attached to ferromagnetic leads is studied in the Kondo regime using a generalized numerical renormalization group technique. We find that the V g dependence of the QD level spin splitting strongly depends on the shape of the density of states ͑DOS͒. For… (More)