Uniform electron gas at finite temperature by fermionic-path-integral Monte Carlo simulations

Филинов, В. С.; Larkin, A. S.; Levashov, P. R.

doi:10.1103/physreve.102.033203

Cited by 21 publications

(22 citation statements)

References 53 publications

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“…. , q (M) } with q (0) = q (M) = 0 after the integration over ξ [18,25] and some additional transformations (see [7,27] for details). The Wigner function can be written in the form of the Maxwell distribution with a quantum correction (if we take into account the sum over only identical and pair permutations):…”

Section: Modifications Of the Path Integral Measure And Exchange Determinantmentioning

confidence: 99%

“…On the other hand, to avoid restrictions of the pair exchange approximation, the Wigner function can be written in a form that allows for the sum over all permutations. Presented below is the approximation based on the approach developed in [7,27], which is the direct generalization of (7) [26]:…”

Section: Modifications Of the Path Integral Measure And Exchange Determinantmentioning

confidence: 99%

“…To account for the Fermi statistics and to overcome the "sign problem" we have modified the path integral representation of Wigner functions and the Monte Carlo method to account for the impact of the interparticle interaction on the Pauli exclusion principle. Our main new contribution to solve this problem is the development of a new approximation for the Wigner function (we used a similar approximation for the density matrix in our previous work [7]), in which exchange determinants are calculated with high accuracy by robust standard algorithms of linear algebra.…”

Section: Introductionmentioning

confidence: 99%

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Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

2022

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The modified path integral representation of Wigner functions and the new Monte Carlo approach has been suggested to account for the impact of the interparticle interaction on the Pauli exclusion principle of fermions. This approach also allows to calculate the momentum distribution functions and to reduce the “sign problem” that is inaccessible to the standard path integral Monte Carlo methods. The obtained pair electron–electron distribution functions for the “uniform electron gas” demonstrate the short-range quantum ordering of electrons associated with exchange–correlation excitons. The exchange–correlation exciton is caused by the interaction of electrons with positively charged exchange holes and the excluded volume effect. The developed approach allows one to study the density–temperature range of the exciton arising, existence, and decay. Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels. The exchange–correlation excitons have not been observed earlier in the standard path integral Monte Carlo simulations.

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Section: Modifications Of the Path Integral Measure And Exchange Determinantmentioning

confidence: 99%

Section: Modifications Of the Path Integral Measure And Exchange Determinantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

2022

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“…Due to the strong electron interaction and absence of small physical parameters we can not use analytical methods based on different perturbation theories and have to deal with the density matrix of the system. Our efforts in this direction have resulted in the development of a new "ab initio" quantum fermionic path integral Monte Carlo approach (FPIMC) [4]. The UEG Hamiltonian contains the electron kinetic K and Coulomb energy Û c ee contributions, the interaction of electrons with the neutralizing background ( Û c ep ) and the self-interaction energy of the background ( Û c pp ).…”

Section: Fermionic Path Integral Monte Carlo Simulationsmentioning

confidence: 99%

“…For electrons, OCP is often called "uniform electron gas" (UEG) or "jellium" and can be used as a model of simple metals. Even though UEG itself does not represent a real physical system, its accurate description is crucial for density functional theory (DFT) [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of the finite-temperature electron gas by the fermionic path integral Monte Carlo method

Filinov,

Levashov,

Larkin

2020

Preprint

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The new ab initio quantum path integral Monte Carlo approach has been developed and applied for the entropy difference calculations for the strongly coupled degenerated uniform electron gas (UEG), a well-known model of simple metals. Calculations have been carried out at finite temperature in canonical ensemble over the wide density and temperature ranges. Obtained data may be crucial for density functional theory. Improvements of the developed approach include the Coulomb and exchange interaction of fermions in the basic Monte Carlo cell and its periodic images and the proper change of variables in the path integral measure. The developed approach shows good agreement with available results for fermions even at temperature four times less than the Fermi energy and practically doesn't suffer from the "fermionic sign problem", which takes place in standard path integral Monte Carlo simulations of degenerate fermionic systems. Presented results include pair distribution functions, isochors and isotherms of pressure, internal energy and entropy change in strongly coupled and degenerate UEG in a wide range of density and temperature.

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Accounting for long–range interaction in the Kelbg pseudopotential

Demyanov

Levashov

2022

Contributions to Plasma Physics

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An expression for the high-temperature density matrix taking into account long-range interaction effects is obtained. The angular averaged Ewald (AAE) potential and Kelbg's solution of the Bloch equation in the first order of perturbation theory are used for this purpose. The expression generalizes the high-temperature density matrix for the Coulomb potential derived earlier by G. Kelbg. An analytical formula for the diagonal Kelbg-AAE pseudopotential is obtained and analysed. The results can be useful in path integral Monte Carlo methods. K E Y W O R D S angular-averaged potential, high-temperature density matrix, Kelbg potential, long-range interaction, path integral Monte Carlo

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Uniform electron gas at finite temperature by fermionic-path-integral Monte Carlo simulations

Cited by 21 publications

References 53 publications

Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

Thermodynamic properties of the finite-temperature electron gas by the fermionic path integral Monte Carlo method

Accounting for long–range interaction in the Kelbg pseudopotential

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