Article

# Quantum phase transitions in the bosonic single-impurity Anderson model

• ##### R. Bulla
Physics of Condensed Matter (Impact Factor: 1.28). 07/2006; 56(3):199-203. DOI: 10.1140/epjb/e2007-00118-3
Source: RePEc

ABSTRACT We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

0 Bookmarks
·
96 Views
• Source
##### Article: Scaling Analysis in the Numerical Renormalization Group Study of the Sub-Ohmic Spin-Boson Model
[Hide abstract]
ABSTRACT: The spin-boson model has nontrivial quantum phase transitions in the sub-Ohmic regime. For the bath spectra exponent $0 \leqslant s<1/2$, the bosonic numerical renormalization group (BNRG) study of the exponents $\beta$ and $\delta$ are hampered by the boson state truncation which leads to artificial interacting exponents instead of the correct Gaussian ones. In this paper, guided by a mean-field calculation, we study the order parameter function $m(\tau=\alpha-\alpha_c, \epsilon, \Delta)$ using BNRG. Scaling analysis with respect to the boson state truncation $N_{b}$, the logarithmic discretization parameter $\Lambda$, and the tunneling strength $\Delta$ are carried out. Truncation-induced multiple-power behaviors are observed close to the critical point, with artificial values of $\beta$ and $\delta$. They cross over to classical behaviors with exponents $\beta=1/2$ and $\delta=3$ on the intermediate scales of $\tau$ and $\epsilon$, respectively. We also find $\tau/\Delta^{1-s}$ and $\epsilon/\Delta$ scalings in the function $m(\tau, \epsilon, \Delta)$. The role of boson state truncation as a scaling variable in the BNRG result for $0 \leqslant s<1/2$ is identified and its interplay with the logarithmic discretization revealed. Relevance to the validity of quantum-to-classical mapping in other impurity models is discussed.
Physical review. B, Condensed matter 12/2010; · 3.77 Impact Factor
• Source
##### Article: Numerical renormalization group for the bosonic single-impurity Anderson model: Dynamics
[Hide abstract]
ABSTRACT: The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization-group calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
Physical review. B, Condensed matter 08/2010; 82(5). · 3.77 Impact Factor
• ##### Article: NRG for the bosonic single-impurity Anderson model: Dynamics
[Hide abstract]
ABSTRACT: The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization group (NRG) calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
04/2010;