Regensburg 2004 – scientific programme
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TT: Tiefe Temperaturen
TT 30: Postersitzung IV: Kritische Ph
änomene, Quantenstörstellen, niederdimensionale Systeme
TT 30.2: Poster
Thursday, March 11, 2004, 14:30–19:00, Poster A
Numerical Renormalization Group Study for Bosonic Systems — •Ninghua Tong1, Ralf Bulla1, and Matthias Vojta2 — 1Theoretische Physik III, Universität Augsburg — 2Institut für Theorie der Kondensierten Materie, Universität Karlsruhe
The physics of an impurity imbedded in a metallic fermionic bath is one of the best studied fields in condensed matter physics. Wilson’s numerical renormalization group (NRG) method has been very successfully applied to such problems due to its non-perturbative nature and the ability to access exponentially small energy scales. In recent years, the physics of impurities in a bosonic bath has attracted much interest. Such systems include impurities imbedded in a magnetic environment and qubits in a dissipative environment. A non-perturbative and accurate method for handling these problems is highly desirable. We propose to generalize Wilson’s NRG method to bosonic systems [R. Bulla, N.-H. Tong, and M. Vojta, Phys. Rev. Lett. 91, 170601 (2003)]. As a first application, we study the spin-boson model, which describes a two-level system coupled linearly to a bath of harmonic oscillators with power law spectral density. We find that the NRG technique works well for this bosonic systems, despite the fact that we have to limit the number of bosons on each site. For the sub-Ohmic bath with exponents 0<S<1, we find clear evidence for a line of continuous quantum phase transitions between localized and delocalized phases. The line terminates in a Kosterlitz-Thouless transition at S=1. Further application to other bosonic impurity problems and the combination with the dynamical mean-field theory for lattice bosonic systems are to be explored.