Towards ab Initio Thermodynamics of the Electron Gas at Strong Degeneracy

Schoof, Tim; Groth, Simon; Bönitz, M.

doi:10.1002/ctpp.201400072

Cited by 45 publications

(59 citation statements)

References 24 publications

(23 reference statements)

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“…III B, and, in a different way, behind the likewise novel density matrix QMC method [34]. The latter approach has recently been applied to the the case of N = 4 spin-polarized electrons [35], where complete agreement with our CPIMC results [24] was reported. These QMC approaches tend to excel at high density, i.e., weak nonideality, and become eventually unfeasible towards stronger coupling strength.…”

Section: Fermionic Quantum Monte Carlo Without Fixed Nodesmentioning

confidence: 64%

“…A detailed derivation of the CPIMC expansion of the partition function and the utilized Monte Carlo steps for the polarized UEG can be found in Refs. [22,24].…”

Section: Basic Ideamentioning

confidence: 99%

“…Thus, if a whole occupied orbital is excited during the MC procedure (for details see Ref. [24]), it can only be excited to an orbital with the same spin projection. For example, orbital 6 in Fig.…”

Section: Application To the Unpolarized Uegmentioning

confidence: 99%

“…[22]) we have combined two novel complementary approaches: our configuration path integral Monte Carlo (CPIMC) method [23][24][25] excels at high to medium density and arbitrary temperature, while our permutation blocking path integral Monte Carlo (PB-PIMC) approach [26,27] significantly extends standard fermionic PIMC [28,29] towards lower temperature and higher density. Surprisingly, it has been found that existing RPIMC results are inaccurate even at high temperatures.…”

Section: Introductionmentioning

confidence: 99%

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Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

et al. 2016

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In a recent publication [S. Groth et al., PRB (2016)], we have shown that the combination of two novel complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo (CPIMC) [T. Schoof et al., PRL 115, 130402 (2015)] and permutation blocking path integral Monte Carlo (PB-PIMC) [T. Dornheim et al., NJP 17, 073017 (2015)], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas (UEG) over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires non-trivial enhancements that we describe in detail. We compare our new simulation results with recent restricted path integral Monte Carlo data [E. Brown et al., PRL 110, 146405 (2013)] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.

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Section: Fermionic Quantum Monte Carlo Without Fixed Nodesmentioning

confidence: 64%

“…A detailed derivation of the CPIMC expansion of the partition function and the utilized Monte Carlo steps for the polarized UEG can be found in Refs. [22,24].…”

Section: Basic Ideamentioning

confidence: 99%

Section: Application To the Unpolarized Uegmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

et al. 2016

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“…Recently, we were able to show [32][33][34] that accurate simulations of these systems are possible over a broad parameter range without any nodal restriction. Our approach combines two independent methods, configuration path-integral Monte Carlo (CPIMC) [35][36][37] and permutation blocking PIMC [38,39], which allow for accurate simulations at high (r s 1) and moderate densities (r s 1 and θ 0.5), respectively. An independently developed third approach, density matrix QMC [40,41], confirmed the excellent quality of these results.…”

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confidence: 99%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

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We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [PRL 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy Fxc of the macroscopic electron gas with an unprecedented accuracy of |∆V |/|V |, |∆Fxc|/|F |xc ∼ 10 −3 . A comparison of our new data to the recent parametrization of Fxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.The uniform electron gas (UEG), consisting of electrons on a uniform neutralizing background, is one of the most important model systems in physics [1]. Besides being a simple model for metals, the UEG has been central to the development of linear response theory and more sophisticated perturbative treatments of solids, the formulation of the concepts of quasiparticles and elementary excitations, and the remarkable successes of density functional theory.The practical application of ground-state density functional theory in condensed matter physics, chemistry and materials science rests on a reliable parametrization of the exchange-correlation energy of the UEG [2], which in turn is based on accurate quantum Monte Carlo (QMC) simulation data [3]. However, the charged quantum matter in astrophysical systems such as planet cores and white dwarf atmospheres [4,5] is at temperatures way above the ground state, as are inertial confinement fusion targets [6][7][8], laser-excited solids [9], and pressure induced modifications of solids, such as insulator-metal transitions [10,11]. This unusual regime, in which strong ionic correlations coexist with electronic quantum effects and partial ionization, has been termed "warm dense matter" and is one of the most active frontiers in plasma physics and materials science.The warm dense regime is characterized by the existence of two comparable length scales and two comparable energy scales. The length scales are the mean interparticle distance,r, and the Bohr radius, a 0 ; the energy scales are the thermal energy, k B T , and the electronic Fermi energy, E F . The dimensionless parameters [12] r s =r/a 0 and Θ = k B T /E F are of order unity. Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-fiel...

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Free energy of the uniform electron gas: Testing analytical models against first‐principles results

Groth

Dornheim

Bönitz

2017

Contributions to Plasma Physics

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The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid‐state systems. However, the simultaneous occurrence of quantum, correlation, and thermal effects makes the theoretical description challenging. For these reasons, over the last half century, many analytical approaches have been developed, the accuracy of which has remained unclear. We have recently obtained the first ab initio data for the exchange correlation free energy of the uniform electron gas, which now provides the opportunity to assess the quality of the mentioned approaches and parameterizations. Particular emphasis is placed on the warm, dense matter regime, where we find significant discrepancies between the different approaches.

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Towards ab Initio Thermodynamics of the Electron Gas at Strong Degeneracy

Cited by 45 publications

References 24 publications

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

Ab initioquantum Monte Carlo simulations of the uniform electron gas without fixed nodes: The unpolarized case

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Free energy of the uniform electron gas: Testing analytical models against first‐principles results

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