1,306 research outputs found

    Two-channel Kondo physics in odd impurity chains

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    We study odd-membered chains of spin-(1/2) impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong inter-impurity coupling, a residual chain spin-(1/2) moment experiences a renormalized effective coupling to the leads; while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models where the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even-fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is non-zero and determined solely by the `excess' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where inter-lead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of these problems.Comment: 21 pages, 19 figure

    Recommending Learning Algorithms and Their Associated Hyperparameters

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    The success of machine learning on a given task dependson, among other things, which learning algorithm is selected and its associated hyperparameters. Selecting an appropriate learning algorithm and setting its hyperparameters for a given data set can be a challenging task, especially for users who are not experts in machine learning. Previous work has examined using meta-features to predict which learning algorithm and hyperparameters should be used. However, choosing a set of meta-features that are predictive of algorithm performance is difficult. Here, we propose to apply collaborative filtering techniques to learning algorithm and hyperparameter selection, and find that doing so avoids determining which meta-features to use and outperforms traditional meta-learning approaches in many cases.Comment: Short paper--2 pages, 2 table

    Two-channel Kondo physics in two-impurity Kondo models

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    We consider the non-Fermi liquid quantum critical state of the spin-S two-impurity Kondo model, and its potential realization in a quantum dot device. Using conformal field theory (CFT) and the numerical renormalization group (NRG), we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin-S. Distinct conductance signatures are shown to arise as a function of device asymmetry; with the `smoking gun' square-root behavior, commonly believed to arise at low-energies, dominant only in certain regimes.Comment: 4.5 pages (with 3 figures) + 9 pages (with 4 figures) supplementary materia

    The History of Air Quality in Utah: A Narrative Review

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    Utah has a rich history related to air pollution; however, it is not widely known or documented. This is despite air quality being a top issue of public concern for the state’s urban residents and acute episodes that feature some of the world’s worst short-term particulate matter exposure. As we discuss in this narrative review, the relationship between air pollution and the state’s residents has changed over time, as fuel sources shifted from wood to coal to petroleum and natural gas. Air pollution rose in prominence as a public issue in the 1880s as Utah’s urban areas grew. Since then, scientific advances have increased the understanding of air quality impacts on human health, groups of concerned citizens worked to raise public awareness, policy makers enacted legislation to improve air quality, and courts upheld rights to clean air. Utah’s air quality future holds challenges and opportunities and can serve as useful case for other urbanizing regions struggling with air quality concerns. Population growth and changing climate will exacerbate current air quality trends, but economically viable clean energy technologies can be deployed to reduce air pollution, bringing substantial public health and economic benefits to the state’s residents and other settings with similar public health concerns

    Generalized Wilson Chain for solving multichannel quantum impurity problems

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    The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a simple generalization of the Wilson Chain, which improves the scaling of computational cost with the number of channels/bands, bringing new problems within reach. The method is applied to calculate the t-matrix of the three-channel Kondo model at T=0, which shows universal crossovers near non-Fermi liquid critical points. A non-integrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening/overscreening mechanisms.Comment: 5 pages + 5 pages supplementary materia
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