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    Tensor networks and the numerical renormalization group

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    The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets intro- duced by Anders and Schiller (2005). In addition, specific attention is given to the possible feedback from low energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-Golden rule calculations (fgrNRG), as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.Comment: 20 pages, 11 figures (adapted from habilitation thesis

    Experience with the Open Source based implementation for ATLAS Conditions Data Management System

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    Conditions Data in high energy physics experiments is frequently seen as every data needed for reconstruction besides the event data itself. This includes all sorts of slowly evolving data like detector alignment, calibration and robustness, and data from detector control system. Also, every Conditions Data Object is associated with a time interval of validity and a version. Besides that, quite often is useful to tag collections of Conditions Data Objects altogether. These issues have already been investigated and a data model has been proposed and used for different implementations based in commercial DBMSs, both at CERN and for the BaBar experiment. The special case of the ATLAS complex trigger that requires online access to calibration and alignment data poses new challenges that have to be met using a flexible and customizable solution more in the line of Open Source components. Motivated by the ATLAS challenges we have developed an alternative implementation, based in an Open Source RDBMS. Several issues were investigated land will be described in this paper: -The best way to map the conditions data model into the relational database concept considering what are foreseen as the most frequent queries. -The clustering model best suited to address the scalability problem. -Extensive tests were performed and will be described. The very promising results from these tests are attracting the attention from the HEP community and driving further developments.Comment: 8 pages, 4 figures, 3 tables, conferenc
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