390 research outputs found
Dynamical conductivity at the dirty superconductor-metal quantum phase transition
We study the transport properties of ultrathin disordered nanowires in the
neighborhood of the superconductor-metal quantum phase transition. To this end
we combine numerical calculations with analytical strong-disorder
renormalization group results. The quantum critical conductivity at zero
temperature diverges logarithmically as a function of frequency. In the
metallic phase, it obeys activated scaling associated with an
infinite-randomness quantum critical point. We extend the scaling theory to
higher dimensions and discuss implications for experiments.Comment: 4 pages, 2 figures; (v2) minor typos corrected, published versio
Efficient simulations of Hartree--Fock equations by an accelerated gradient descent method
We develop convergence acceleration procedures that enable a gradient
descent-type iteration method to efficiently simulate Hartree--Fock equations
for atoms interacting both with each other and with an external potential. Our
development focuses on three aspects: (i) optimization of a parameter in the
preconditioning operator; (ii) adoption of a technique that eliminates the
slowest-decaying mode to the case of many equations (describing many atoms);
and (iii) a novel extension of the above technique that allows one to eliminate
multiple modes simultaneously. We illustrate performance of the numerical
method for the 2D model of the first layer of helium atoms above a graphene
sheet. We demonstrate that incorporation of aspects (i) and (ii) above into the
``plain" gradient descent method accelerates it by at least two orders of
magnitude, and often by much more. Aspect (iii) -- a multiple-mode elimination
-- may bring further improvement to the convergence rate compared to aspect
(ii), the single-mode elimination. Both single- and multiple-mode elimination
techniques are shown to significantly outperform the well-known Anderson
Acceleration. We believe that our acceleration techniques can also be gainfully
employed by other numerical methods, especially those handling hard-core-type
interaction potentials.Comment: main text (39 pages); supplement appended (7 pages
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