Progress in Study of Equation of State of Warm Dense Matter with Path-integral Monte Carlo Method

doi:10.19596/j.cnki.1001-246x.8599

Abstract

Abstract:

In this paper, the basic framework of PIMC method is firstly described in detail. In particular, four techniques developed for PIMC simulations to deal with the Fermi sign problem are reviewed. EOS data of various WDM systems obtained with PIMC simulations are then summarized, with which the advantages and disadvantages of PIMC method are illustrated. Finally, some future prospects of PIMC method are discussed.

Key words: warm dense matter, equation of state, path-integral Monte Carlo

Zixiang YAN, Wei KANG, Weiyan ZHANG, Xiantu HE. Progress in Study of Equation of State of Warm Dense Matter with Path-integral Monte Carlo Method[J]. Chinese Journal of Computational Physics, 2023, 40(2): 258-274.

Figures/Tables 8

Fig.1 The ranges of applicability for different PIMC method in the study of UEG (The density parameter $ r_{\mathrm{s}}=a / a_0$ with a the average distance of electrons and a0 the Bohr radius, and the temperature parameter $\varTheta=T / T_{\mathrm{F}} $ with TF the Fermi temperature.)

Fig.2 Hugoniot curve of deuterium calculated with RPIMC method[47] (Data points in different colors and marks represent the results calculated with different time steps τ, particle number N and nodal types.)

Fig.3 Temperature dependence of deuterium's pressure at constant density of (a) ρ = 10.00 g ·cm-3 and (b) ρ = 1 596.49 g ·cm-3 (The black circles stand for the RPIMC results[47], while the red squares represent the DPIMC results[46].)

Fig.4 Hugoniot curve of deuterium calculated with DPIMC method[86], as represented by the red dashed curve. The results of RPIMC simulation[47] are also presented with the black curve, for the comparison purpose

Fig.5 (a) Temperature dependence of internal energy of a single silicon atom[61] (Periodic cell of 5.0 Bohr is employed in simulation. The data points in different marks represent the results calculated with different nodes. The density functional theory (DFT) results are also shown as the reference, as represented by the black crosses.); (b) Temperature dependence of pressure of a single silicon atom

Fig.6 Hugoniot curves of middle Z materials. (a) Hugoniot curve of Boron (The black curve and blue circles represent the results of RPIMC+DFT-MD[51] and experiments[51].); (b) Hugoniot curve of Sodium (The black curve and blue squares represent the results of RPIMC+DFT-MD[57] and the experiments cited within Ref. [57].); (c) Hugoniot curve of Aluminum (The black curve, red dashed curve and blue squares represent the results of RPIMC+DFT-MD[60], ext-FPMD[23] and the experiments cited within Ref. [60].); (d) Hugoniot curve of Silicon (The black curve, red dashed curve and blue squares represent the results of RPIMC+DFT-MD[62], OFMD+DFT-MD[62] and the experiments cited within Ref. [62].)

Fig.7 Hugoniot curve of Hydrocarbon (CH) (The black curve, red circles, green squares, and blue diamonds represent the results of RPIMC+DFT-MD[66], ext-FPMD[24], DFT-MD[88] and OFMD[88], respectively.)

Fig.8 (a) Hugoniot curve of boron nitride (BN)[89] (The red curve represents the direct result of BN through RPIMC simulations with an initial density of 2.26g ·cm-3. The blue dash dot line represents the result with linear mixed approximation of elemental B and N.); (b) Hugoniot curve of magnesium silicate (MgSiO3)[89] (The red curve represents the RPIMC result of MgSiO3 with an initial density of 3.208 g ·cm-3, while the green dash dot curve represents the result with linear mixed approximation of elemental Mg, Si, and O.)

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