Article
Quantum phase transitions in the bosonic singleimpurity Anderson model
Physics of Condensed Matter (Impact Factor: 1.28). 07/2006; 56(3):199203. DOI: 10.1140/epjb/e2007001183
Source: RePEc

Article: Scaling Analysis in the Numerical Renormalization Group Study of the SubOhmic SpinBoson Model
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ABSTRACT: The spinboson model has nontrivial quantum phase transitions in the subOhmic 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 meanfield 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. Truncationinduced multiplepower 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 $\tau/\Delta^{1s}$ 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 quantumtoclassical mapping in other impurity models is discussed.Physical review. B, Condensed matter 12/2010; · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The bosonic singleimpurity Anderson model (BSIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a BoseEinstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalizationgroup calculation for the BSIAM revealed a zerotemperature 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 BSIAM 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  [Show abstract] [Hide abstract]
ABSTRACT: The bosonic singleimpurity Anderson model (BSIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a BoseEinstein 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 BSIAM revealed a zerotemperature 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 BSIAM which reinforce our understanding of the physics in the Mott and the BEC phases.04/2010;
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