Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains

Ryszard Matysiak; Philipp Gegenwart; Akira Ochiai; Frank Steglich

doi:10.1007/978-3-319-78054-2_34

Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains

Ryszard Matysiak, Philipp Gegenwart, Akira Ochiai, Frank Steglich

SCI - Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers
Editors	Ewa Deelman, Roman Wyrzykowski, Konrad Karczewski, Jack Dongarra
Publisher	Springer Verlag
Pages	359-367
Number of pages	9
ISBN (Print)	9783319780535
DOIs	https://doi.org/10.1007/978-3-319-78054-2_34
Publication status	Published - 2018
Event	12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017 - Czestochowa, Poland Duration: 2017 Sept 10 → 2017 Sept 13

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10778 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017
Country/Territory	Poland
City	Czestochowa
Period	17/9/10 → 17/9/13

Keywords

One-dimensional spin chains
Quantum transfer-matrix method
Segmented heisenberg antiferromagnet

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-319-78054-2_34

Cite this

Matysiak, R., Gegenwart, P., Ochiai, A., & Steglich, F. (2018). Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains. In E. Deelman, R. Wyrzykowski, K. Karczewski, & J. Dongarra (Eds.), Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers (pp. 359-367). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10778 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-78054-2_34

Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains. / Matysiak, Ryszard; Gegenwart, Philipp; Ochiai, Akira et al.

Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. ed. / Ewa Deelman; Roman Wyrzykowski; Konrad Karczewski; Jack Dongarra. Springer Verlag, 2018. p. 359-367 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10778 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Matysiak, R, Gegenwart, P, Ochiai, A & Steglich, F 2018, Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains. in E Deelman, R Wyrzykowski, K Karczewski & J Dongarra (eds), Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10778 LNCS, Springer Verlag, pp. 359-367, 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, Czestochowa, Poland, 17/9/10. https://doi.org/10.1007/978-3-319-78054-2_34

Matysiak R, Gegenwart P, Ochiai A, Steglich F. Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains. In Deelman E, Wyrzykowski R, Karczewski K, Dongarra J, editors, Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. Springer Verlag. 2018. p. 359-367. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-78054-2_34

Matysiak, Ryszard ; Gegenwart, Philipp ; Ochiai, Akira et al. / Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains. Parallel Processing and Applied Mathematics - 12th International Conference, PPAM 2017, Revised Selected Papers. editor / Ewa Deelman ; Roman Wyrzykowski ; Konrad Karczewski ; Jack Dongarra. Springer Verlag, 2018. pp. 359-367 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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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author = "Ryszard Matysiak and Philipp Gegenwart and Akira Ochiai and Frank Steglich",

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AU - Matysiak, Ryszard

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AU - Ochiai, Akira

AU - Steglich, Frank

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

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N2 - 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.

AB - 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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Application of numerical quantum transfer-matrix approach in the randomly diluted quantum spin chains

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