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Quantum Monte Carlo Techniques and Applications for Warm Dense Matter

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Frontiers and Challenges in Warm Dense Matter

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 96))

Abstract

The Quantum Monte Carlo (QMC) method is used to study physical problems which are analytically intractable due to many-body interactions and strong coupling strengths. This makes QMC a natural choice in the warm dense matter (WDM) regime where both the Coulomb coupling parameter \(\varGamma \equiv {e}^{2}/(r_{s}k_{B}T)\) and the electron degeneracy parameter Θ ≡ T∕T F are close to unity. As a truly first-principles simulation method, it affords superior accuracy while still maintaining reasonable scaling, emphasizing its role as a benchmark tool.Here we give an overview of QMC methods including diffusion MC, path integral MC, and coupled electron-ion MC. We then provide several examples of their use in the WDM regime, reviewing applications to the electron gas, hydrogen plasma, and first row elements. We conclude with a comparison of QMC to other existing methods, touching specifically on QMC’s range of applicability.

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Notes

  1. 1.

    See Sect. 1.4 for more details on wave functions and optimization methods.

  2. 2.

    Note that this assumes real wave functions. If otherwise, the fixed-phase approximation may be used [4].

  3. 3.

    Note, for non-diagonal elements the sum over odd permutations must be retained.

  4. 4.

    All exact methods that work with finite systems share this difficulty.

  5. 5.

    All data can be found in a repository hosted at http://github.com/3dheg/3DHEG

  6. 6.

    Note that both theories are compatible with experiments because of the large uncertainty of the latter.

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Acknowledgements

DC is supported by DOE DE-NA0001789. EB is supported by DOE DE-AC52-07NA27344, LDRD 10-ERD-058 and the LLNL Lawrence Scholar program. CP is supported by the Italian Institute of Technology (IIT) under the SEED project grant number 259 SIMBEDD Advanced Computational Methods for Biophysics, Drug Design and Energy Research. This work was performed in part under the auspices of the US DOE by LLNL under Contract DE-AC52-07NA27344.

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Authors and Affiliations

  1. Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA, 94550, USA

    Ethan Brown & Miguel A. Morales

  2. Department of Physics, University of Illinois Urbana-Champaign, 1110 W. Green St., Urbana, IL, 61801-3080, USA

    Ethan Brown & David Ceperley

  3. Dipartimento di Scienze Fisiche e Chimiche, Universita dell’Aquila and CNISM, UdR dell’Aquila, a V. Vetoio 10, Loc. Coppito, I-67100, L’Aquila, Italy

    Carlo Pierleoni

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  1. Ethan Brown
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  2. Miguel A. Morales
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Correspondence to David Ceperley .

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Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, California, USA

    Frank Graziani

  2. Sandia National Laboratories, Albuquerque, New Mexico, USA

    Michael P. Desjarlais

  3. Institute of Physics, University of Rostock, Rostock, Germany

    Ronald Redmer

  4. Department of Physics, University of Florida, Gainesville, Florida, USA

    Samuel B. Trickey

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Brown, E., Morales, M.A., Pierleoni, C., Ceperley, D. (2014). Quantum Monte Carlo Techniques and Applications for Warm Dense Matter. In: Graziani, F., Desjarlais, M., Redmer, R., Trickey, S. (eds) Frontiers and Challenges in Warm Dense Matter. Lecture Notes in Computational Science and Engineering, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-04912-0_5

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