On the Thermodynamics of Fermions at any Temperature based on Parametrized Partition Function

Xiong, Hongwei; Xiong, Yunuo

doi:10.20944/preprints202211.0404.v1

Cited by 3 publications

(15 citation statements)

References 40 publications

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“…Here, we will give the result of the energy estimator for the fictitious identical particles, with the application of the virial theorem. Even for identical bosons with parameter ξ = 1, we emphasize that the present virial estimator for energy is an important improvement, compared with the previous works 14,15,19,20 , where the virial theorem is not used.…”

Section: The Thermodynamics Of Fictitious Identical Particles With Pimdmentioning

confidence: 74%

“…The above isothermal extrapolation method 14 has been shown to be highly efficient and accurate for simulating medium-scale and large-scale Fermi systems in the case of weak quantum degeneracy 16,17 . A further improvement is the constant energy semi-extrapolation 15 , which can be used to efficiently and accurately simulate the energy of fermions from zero temperature (high quantum degeneracy) to medium and high temperature (moderate and weak quantum degeneracy).…”

Section: B Isothermal Extrapolationmentioning

confidence: 99%

“…In principle, the constant energy semi-extrapolation method is more accurate and has a wider range of applicability than the isothermal extrapolation method. One of the reasons is that in the constant energy semi-extrapolation, we can also use the following exact properties 15 :…”

Section: Constant Energy Semi-extrapolationmentioning

confidence: 99%

“…Unfortunately, for PIMC/PIMD, when simulating fermions, the fermion sign problem [9][10][11][12][13] poses a serious obstacle, and the computational cost increases exponentially with the number of fermions or the decrease in temperature. Recently, we used the idea of fictitious identical particles 14,15 to try to overcome the fermion sign problem, and found that it is indeed promising to accurately simulate the thermodynamic properties of many important fermionic systems from zero temperature to high temperature, and the computational complexity is no different from the case of bosons. Afterwards, the idea of fictitious identical particles for overcoming the fermion sign problem was systematically verified and confirmed by Dornheim et al 16 , and after extending the applicability of fictitious identical particles, they highly accurately simulated the static structure factor and static linear density response function of warm dense matter with one thousand fermions 17 .…”

Section: Introductionmentioning

confidence: 99%

“…The computational complexity of simulating fermionic systems in the fictitious identical particle PIMC framework is O(N 2 ) 16,17 . In the initial paper 14,15 on fictitious identical particle PIMD, we used the recursion formula for bosonic PIMD developed by Hirsheberg et al 19 , to simulate fermionic systems with a computational complexity of O(P N 3 ). From the efficiency perspective, fictitious identical particle PIMD and the corresponding PIMC are still not competitive.…”

Section: Introductionmentioning

confidence: 99%

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Competition Mathematics as a Complement and Enhancement for In-Class Instruction

Xiong

2021

School Mathematics Textbooks in China

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Section: The Thermodynamics Of Fictitious Identical Particles With Pimdmentioning

confidence: 74%

Section: B Isothermal Extrapolationmentioning

confidence: 99%

Section: Constant Energy Semi-extrapolationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Competition Mathematics as a Complement and Enhancement for In-Class Instruction

Xiong

2021

School Mathematics Textbooks in China

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On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem

Xiong

2022

The Journal of Chemical Physics

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By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature <p>thermodynamic properties of fictitious identical particles with a real parameter ξ interpolating continuously between bosons (ξ=1) and fermions (ξ=-1). Through general analysis and numerical experiments we find that the average energy may have good analytical property as a function of this real parameter ξ, which provides the chance to calculate the thermodynamical properties of identical fermions by an extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for ξ{greater than or equal to}0. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion sign problem for some quantum systems.

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Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

Dornheim

Moldabekov

Vorberger

et al. 2020

Plasma Phys. Control. Fusion

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The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [J. Chem. Phys. 151, 194104 (2019)] and strongly coupled electron liquid [Phys. Rev. B 101, 045129 (2020)] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of 0.05 ≤ r s ≤ 0.5 and 0.85 ≤ θ ≤ 8. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of 0.001 − 0.01%. All PIMC data are available online.The Uniform Electron Gas in the High Density Regime 2 IntroductionThe uniform electron gas (UEG), also known as jellium or quantum one-component plasma, is defined as a system of Coulomb interacting electrons in a neutralizing homogeneous background and constitutes one of the most import model systems in physics and chemistry [1,2,3]. Having been introduced as a simple model description for conduction electrons in metals [4], the UEG exhibits a variety of interesting effects, such as Wigner crystallization [5,6,7] and a possible incipient excitonic mode which has been predicted to appear at low density [8,9,10,11].Moreover, the availability of highly accurate quantum Monte Carlo (QMC) data [12,13,14,15,16] at metallic densities and zero-temperature has sparked remarkable developments in many fields, most notably the hitherto unequaled success of density functional theory (DFT) regarding the description of real materials [17,18].Recently, the interest in matter under extreme conditions [19] has led to the need for analogous quantum Monte Carlo data at finite temperature. Of particular importance is the so-called warm dense matter (WDM) regime, which is defined by two characteristic parameters that are both of the order of one: i) the density parameter r s = r/a B (with r and a B being the average inter-particle distance and first Bohr radius) and ii) the reduced temperature θ = k B T /E F (with k B and E F being the Boltzmann constant and Fermi energy [1]), cf. Fig. 1 below. These conditions occur in astrophysical objects like giant planet interiors [20,21,22] and are expected to manifest on the pathway towards inertial confinement fusion [23]. Furthermore, WDM is nowadays routinely realized in large research facilities around the globe like the Linac Coherent Light Source (LCLS) [24], the National Ignition Facility (NIF) [25], and th...

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On the Thermodynamics of Fermions at any Temperature based on Parametrized Partition Function

Cited by 3 publications

References 40 publications

Competition Mathematics as a Complement and Enhancement for In-Class Instruction

Competition Mathematics as a Complement and Enhancement for In-Class Instruction

On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem

Ab initio path integral monte carlo simulation of the uniform electron gas in the high energy density regime

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