590 research outputs found
Self-Consistent Perturbation Theory for Thermodynamics of Magnetic Impurity Systems
Integral equations for thermodynamic quantities are derived in the framework
of the non-crossing approximation (NCA). Entropy and specific heat of 4f
contribution are calculated without numerical differentiations of thermodynamic
potential. The formulation is applied to systems such as PrFe4P12 with
singlet-triplet crystalline electric field (CEF) levels.Comment: 3 pages, 2 figures, proc. ASR-WYP-2005 (JAERI
The Hubbard Model at Infinite Dimensions: Thermodynamic and Transport Properties
We present results on thermodynamic quantities, resistivity and optical
conductivity for the Hubbard model on a simple hypercubic lattice in infinite
dimensions. Our results for the paramagnetic phase display the features
expected from an intuitive analysis of the one-particle spectra and
substantiate the similarity of the physics of the Hubbard model to those of
heavy fermion systems. The calculations were performed using an approximate
solution to the single-impurity Anderson model, which is the key quantity
entering the solution of the Hubbard model in this limit. To establish the
quality of this approximation we compare its results, together with those
obtained from two other widely used methods, to essentially exact quantum Monte
Carlo results.Comment: 29 pages, 16 figure
Adaptive optimization for OpenCL programs on embedded heterogeneous systems
Heterogeneous multi-core architectures consisting of CPUs and GPUs are commonplace in today’s embedded systems. These architectures offer potential for energy efficient computing if the application task is mapped to the right core. Realizing such potential is challenging due to the complex and evolving nature of hardware and applications. This paper presents an automatic approach to map OpenCL kernels onto heterogeneous multi-cores for a given optimization criterion – whether it is faster runtime, lower energy consumption or a trade-off between them. This is achieved by developing a machine learning based approach to predict which processor to use to run the OpenCL kernel and the host program, and at what frequency the processor should operate. Instead of hand-tuning a model for each optimization metric, we use machine learning to develop a unified framework that first automatically learns the optimization heuristic for each metric off-line, then uses the learned knowledge to schedule OpenCL kernels at runtime based on code and runtime information of the program. We apply our approach to a set of representative OpenCL benchmarks and evaluate it on an ARM big.LITTLE mobile platform. Our approach achieves over 93% of the performance delivered by a perfect predictor.We obtain, on average, 1.2x, 1.6x, and 1.8x improvement respectively for runtime, energy consumption and the energy delay product when compared to a comparative heterogeneous-aware OpenCL task mapping scheme
Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems
For the treatment of interacting electrons in crystal lattices approximations
based on the picture of effective sites, coupled in a self-consistent fashion,
have proven very useful. Particularly in the presence of strong local
correlations, a local approach to the problem, combining a powerful method for
the short ranged interactions with the lattice propagation part of the
dynamics, determines the quality of results to a large extent. For a
considerable time the non crossing approximation (NCA) in direct perturbation
theory, an approach originally developed by Keiter for the Anderson impurity
model, built a standard for the description of the local dynamics of
interacting electrons. In the last couple of years exact methods like the
numerical renormalization group (NRG) as pioneered by Wilson, have surpassed
this approximation as regarding the description of the low energy regime. We
present an improved approximation level of direct perturbation theory for
finite Coulomb repulsion U, the crossing approximation one (CA1) and discuss
its connections with other generalizations of NCA. CA1 incorporates all
processes up to fourth order in the hybridization strength V in a
self-consistent skeleton expansion, retaining the full energy dependence of the
vertex functions. We reconstruct the local approach to the lattice problem from
the point of view of cumulant perturbation theory in a very general way and
discuss the proper use of impurity solvers for this purpose. Their reliability
can be tested in applications to e.g. the Hubbard model and the
Anderson-lattice model. We point out shortcomings of existing impurity solvers
and improvements gained with CA1 in this context.
This paper is dedicated to the memory of Hellmut Keiter.Comment: 45 pages, 22 figure
Dynamic susceptibilities of the single impurity Anderson model within an enhanced non-crossing approximation
The single impurity Anderson model (SIAM) is studied within an enhanced
non-crossing approximation (ENCA). This method is extended to the calculation
of susceptibilities and thoroughly tested, also in order to prepare
applications as a building block for the calculation of susceptibilities and
phase transitions in correlated lattice systems. A wide range of model
parameters, such as impurity occupancy, temperature, local Coulomb repulsion
and hybridization strength, are studied. Results for the spin and charge
susceptibilities are presented. By comparing the static quantities to exact
Bethe ansatz results, it is shown that the description of the magnetic
excitations of the impurity within the ENCA is excellent, even in situations
with large valence fluctuations or vanishing Coulomb repulsion. The description
of the charge susceptibility is quite accurate in situations where the singly
occupied ionic configuration is the unperturbed ground state; however, it seems
to overestimate charge fluctuations in the asymmetric model at too low
temperatures. The dynamic spin excitation spectra is dominated by the
Kondo-screening of the impurity spin through the conduction band, i.e. the
formation of the local Kondo-singlet. A finite local Coulomb interaction U
leads to a drastic reduction of the charge response via processes involving the
doubly occupied impurity state. In the asymmetric model, the charge
susceptibility is enhanced for excitation energies smaller than the Kondo scale
T_K due to the influence of valence fluctuations.Comment: 16 pages, 13 figure
Field-induced phase transitions in a Kondo insulator
We study the magnetic-field effect on a Kondo insulator by exploiting the
periodic Anderson model with the Zeeman term. The analysis using dynamical mean
field theory combined with quantum Monte Carlo simulations determines the
detailed phase diagram at finite temperatures. At low temperatures, the
magnetic field drives the Kondo insulator to a transverse antiferromagnetic
phase, which further enters a polarized metallic phase at higher fields. The
antiferromagnetic transition temperature takes a maximum when the Zeeman
energy is nearly equal to the quasi-particle gap. In the paramagnetic phase
above , we find that the electron mass gets largest around the field where
the quasi-particle gap is closed. It is also shown that the induced moment of
conduction electrons changes its direction from antiparallel to parallel to the
field.Comment: 7 pages, 6 figure
Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation
The two-particle-self-consistent theory is applied to the single-impurity
Anderson model. It is found that it cannot reproduce the small energy scale in
the strong correlation limit. A modified scheme to overcome this difficulty is
proposed by introducing an appropriate vertex correction explicitly. Using the
same vertex correction, the self-energy is investigated, and it is found that
under certain assumptions it reproduces the result of the modified perturbation
theory which interpolates the weak and the strong correlation limits.Comment: 5 pages, 7 figures, submitted to J. Phys. Soc. Jp
Heavy-Fermions in LiV2O4: Kondo-Compensation vs. Spin-Liquid Behavior?
7Li NMR measurements were performed in the metallic spinel LiV2O4. The
temperature dependencies of the line width, the Knight shift and the
spin-lattice relaxation rate were investigated in the temperature range 30 mK <
T < 280 K. For temperatures T < 1 K we observe a spin-lattice relaxation rate
which slows down exponentially. The NMR results can be explained by a
spin-liquid behavior and the opening of a spin gap of the order 0.6 K
The Kondo Box: A Magnetic Impurity in an Ultrasmall Metallic Grain
We study the Kondo effect generated by a single magnetic impurity embedded in
an ultrasmall metallic grain, to be called a ``Kondo box''. We find that the
Kondo resonance is strongly affected when the mean level spacing in the grain
becomes larger than the Kondo temperature, in a way that depends on the parity
of the number of electrons on the grain. We show that the single-electron
tunneling conductance through such a grain features Kondo-induced Fano-type
resonances of measurable size, with an anomalous dependence on temperature and
level spacing.Comment: 4 Latex pages, 4 figures, submitted to Phys. Rev. Let
Excitonic Bound State in the Extended Anderson Model with c-f Coulomb Interaction
The Anderson model with the Coulomb interaction between the local and
conduction electrons is studied in the semiconducting phase. Based on a
perturbation theory from the atomic limit, leading contributions for the c-f
Coulomb interaction are incorporated as a vertex correction to hybridization.
An analytical solution shows that the effective attraction in the intermediate
states leads to a bound state localized at the local electron site.
Self-consistent equations are constructed as an extension of the non-crossing
approximation (NCA) to include the vertex part yielding the bound state. A
numerical calculation demonstrates the excitonic bound state inside the
semiconducting gap for single-particle excitations, and a discontinuity at the
gap edge for magnetic excitations.Comment: 15 pages, 20 figures, submitted to J. Phys. Soc. Jp
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