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International Conference on Parallel Processing and Applied Mathematics

PPAM 2017: Parallel Processing and Applied Mathematics pp 359–367Cite as

Application of Numerical Quantum Transfer-Matrix Approach in the Randomly Diluted Quantum Spin Chains

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10778))

Abstract

The description of the numerical method of simulation based on the quantum transfer-matrix (QTM) approach is presented for diluted spin \(S=1/2\) chains. Modification of the extrapolation technique has been used to obtain better accuracy of numerical results. The simulations have been performed using the \(S=1/2\) antiferromagnetic Heisenberg model with the transverse staggered field and a uniform magnetic field perpendicular to the staggered field applicable for the diluted compound (Yb\(_{1-x}\)Lu\(_x\))\(_4\)As\(_3\). In the model calculations the fixed microscopic parameters established earlier for the pure system have been assumed and the random impurity distribution has been considered. The experimental field-dependent specific heat of the polydomain diluted (Yb\(_{1-x}\)Lu\(_x\))\(_4\)As\(_3\) sample is compared with that calculated using the HPC resources and providing additional verification of both the QTM method and the physical model.

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Acknowledgement

We thank for an access to the HPC resources in PSNC Poznań (Poland).

Author information

Authors and Affiliations

  1. Institute of Engineering and Computer Education, University of Zielona Góra, ul. prof. Z. Szafrana 4, 65-516, Zielona Góra, Poland

    Ryszard Matysiak

  2. Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany

    Philipp Gegenwart & Frank Steglich

  3. Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159, Augsburg, Germany

    Philipp Gegenwart

  4. Center for Low Temperature Science, Tohoku University, Sendai, 980-8578, Japan

    Akira Ochiai

Authors
  1. Ryszard Matysiak
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  2. Philipp Gegenwart
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  3. Akira Ochiai
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  4. Frank Steglich
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Corresponding author

Correspondence to Ryszard Matysiak .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Matysiak, R., Gegenwart, P., Ochiai, A., Steglich, F. (2018). Application of Numerical Quantum Transfer-Matrix Approach in the Randomly Diluted Quantum Spin Chains. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10778. Springer, Cham. https://doi.org/10.1007/978-3-319-78054-2_34

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  • DOI: https://doi.org/10.1007/978-3-319-78054-2_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78053-5

  • Online ISBN: 978-3-319-78054-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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