Article

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

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

Source: RePEc

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**ABSTRACT:**We show how exact diagonalization of small clusters can be used as a fast and reliable impurity solver by determining the phase diagram and physical properties of the bosonic single-impurity Anderson model. This is specially important for applications which require the solution of a large number of different single-impurity problems, such as the bosonic dynamical mean field theory of disordered systems. In particular, we investigate the connection between spontaneous global gauge symmetry breaking and the occurrence of Bose-Einstein condensation (BEC). We show how BEC is accurately signaled by the appearance of broken symmetry, even when a fairly modest number of states is retained. The occurrence of symmetry breaking can be detected both by adding a small conjugate field or, as in generic quantum critical points, by the divergence of the associated phase susceptibility. Our results show excellent agreement with the considerably more demanding numerical renormalization group (NRG) method. We also investigate the mean impurity occupancy and its fluctuations, identifying an asymmetry in their critical behavior across the quantum phase transitions between BEC and ‘Mott’ phases.Physics of Condensed Matter 01/2012; 85(10). · 1.28 Impact Factor -
##### Article: Scaling Analysis in the Numerical Renormalization Group Study of the Sub-Ohmic Spin-Boson Model

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**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 - [Show abstract] [Hide abstract]

**ABSTRACT:**We study nonequilibrium properties of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) within Keldysh-Green's function formalism when the AQD level is varied harmonically in time. Nonequilibrium features in the AQD energy absorption spectrum are the side peaks that develop as an effect of photon absorption and emission. We show that atoms can be efficiently transferred from the BEC into the AQD for the parameter regime of current experiments with cold atoms.The European Physical Journal Special Topics 01/2013; 217:55. · 1.80 Impact Factor

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