Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.16088

Scaling law for the size dependence of a finite-range quantum gas

Luigi Delle Site, Carsten Hartmann

Published Aug 30, 2023• 0 citations
arXivHTMLPDF

Abstract

In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has been shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts, can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite range interactions that models a dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.

DOI
10.48550/arxiv.2308.16088

Related papers

Scaling law for the size dependence of a finite-range quantum gas

Luigi Delle Site, Carsten Hartmann

In a recent work [Reible et al., Phys. Rev. Res. 5, 023156 (2023)], it was shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite-range interactions that model dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free-energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.

Physical Review A•Feb 9, 2024•3 citations

Finite-size effects and thermodynamic accuracy in many-particle systems

Benedikt M. Reible, Julian F. Hille, Carsten Hartmann +1 more

Finite-size effects arise when a sample of particles is not sufficient to provide a statistically satisfactory description of the bulk environment of a physical system. As a consequence, a reliable estimate of finite-size effects in many-particle systems is key to judge the validity of a theoretical model or the accuracy of a numerical simulation. In this context, we propose the use of a theorem on the free-energy cost for separating a system into smaller independent subsystems [J. Stat. Mech.: Theory Exp. (2017) 083201; Lett. Math. Phys. 112, 97 (2022)] to estimate the relevance of finite-size effects in thermodynamic quantities from computer simulations. The key aspect of this study is that for two-body potentials, as mostly occurring in physics, the method requires only two-body distribution functions and the particle number density. The calculation of the involved physical quantities can be done numerically on a three-dimensional grid. In some cases even analytical estimates are possible and as an example the uniform interacting electron gas in the ground state is considered; we derive an approximating scaling law for the finite-size effects.

Physical Review Research•Jun 9, 2023•12 citations

Two-sided Bogoliubov inequality to estimate finite size effects in quantum molecular simulations

Benedikt M. Reible, Carsten Hartmann, Luigi Delle Site

Abstract We generalise the two-sided Bogoliubov inequality for classical particles (Delle Site et al. in J Stat Mech Theory Exp 083201, 2017 to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower bounds for the free energy difference associated with the partitioning of a large system into smaller, independent subsystems. From a thermodynamic modelling point of view, the free energy difference determines the finite size correction needed to consistently treat a small system as a representation of a large system. Applications of the bounds to quantify finite size effects are ubiquitous in physics, chemistry, material science, or biology, to name just a few; in particular, it is relevant for molecular dynamics simulations in which a small portion of a system is usually taken as representative of the idealized large system.

arXiv:2111.10282•Letters in Mathematical Physics•Sep 21, 2022•6 citations

Overcoming finite-size effects in electronic structure simulations at extreme conditions

Tobias Dornheim, Jan Vorberger

Ab initio quantum Monte Carlo methods, in principle, allow for the calculation of exact properties of correlated many-electron systems but are, in general, limited to the simulation of a finite number of electrons N under periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas at finite temperature, as it is relevant to contemporary research, e.g., in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor S(q) and in the interaction energy v, which is based on the density response formalism. We demonstrate that this method often allows us to obtain v in the thermodynamic limit within a relative accuracy of ∼0.2% from as few as N = 4 electrons without any empirical choices or knowledge of results for other values of N. Finally, we evaluate the applicability of our method upon increasing the density parameter rs and decreasing the temperature T.

arXiv:2101.11364•The Journal of Chemical Physics•Apr 8, 2021•42 citations

Finite-size effects in the ideal Fermi gas

V. Subrahmanyam, Mustansir Barma

The ideal Fermi gas in a finite volume is studied in the low-temperature regime where the thermal correlation length is comparable to the size L of the system. Physical quantities such as the density of fermions and the appropriate ordering susceptibility show oscillatory fluctuations around a smooth background as L is varied. These are investigated numerically and analytically. The amplitude of the fluctuations depends on the observable in question and on the container shape. Finite-size scaling does not hold directly for thermodynamic quantities but is recoverable by averaging the mean-squared fluctuations over an appropriate range in L.

Journal of Physics A Mathematical and General•Jun 7, 1989•13 citations

Renormalization factor and effective mass of the two-dimensional electron gas

Markus Holzmann, B. Bernu, Valério Olevano +2 more

We calculate the momentum distribution of the Fermi-liquid phase of the homogeneous two-dimensional electron gas. We show that close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its thermodynamic limit slowly, with leading-order corrections scaling as ${N}^{\ensuremath{-}1/4}$. These corrections dominate the extrapolation of the renormalization factor $Z$ and the single-particle effective mass ${m}^{\ensuremath{\ast}}$ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range $1\ensuremath{\le}{r}_{s}\ensuremath{\le}10$, we get a lower renormalization factor $Z$ and a higher effective mass ${m}^{\ensuremath{\ast}}>m$ compared to the perturbative random-phase approximation values.

arXiv:0810.2450•Physical Review B•Jan 30, 2009•45 citations
In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has been shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts, can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite range interactions that models a dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.
In a recent work [Reible et al., Phys. Rev. Res. 5, 023156 (2023)], it was shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite-range interactions that model dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free-energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.
Finite-size effects arise when a sample of particles is not sufficient to provide a statistically satisfactory description of the bulk environment of a physical system. As a consequence, a reliable estimate of finite-size effects in many-particle systems is key to judge the validity of a theoretical model or the accuracy of a numerical simulation. In this context, we propose the use of a theorem on the free-energy cost for separating a system into smaller independent subsystems [J. Stat. Mech.: Theory Exp. (2017) 083201; Lett. Math. Phys. 112, 97 (2022)] to estimate the relevance of finite-size effects in thermodynamic quantities from computer simulations. The key aspect of this study is that for two-body potentials, as mostly occurring in physics, the method requires only two-body distribution functions and the particle number density. The calculation of the involved physical quantities can be done numerically on a three-dimensional grid. In some cases even analytical estimates are possible and as an example the uniform interacting electron gas in the ground state is considered; we derive an approximating scaling law for the finite-size effects.
Abstract We generalise the two-sided Bogoliubov inequality for classical particles (Delle Site et al. in J Stat Mech Theory Exp 083201, 2017 to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower bounds for the free energy difference associated with the partitioning of a large system into smaller, independent subsystems. From a thermodynamic modelling point of view, the free energy difference determines the finite size correction needed to consistently treat a small system as a representation of a large system. Applications of the bounds to quantify finite size effects are ubiquitous in physics, chemistry, material science, or biology, to name just a few; in particular, it is relevant for molecular dynamics simulations in which a small portion of a system is usually taken as representative of the idealized large system.
Ab initio quantum Monte Carlo methods, in principle, allow for the calculation of exact properties of correlated many-electron systems but are, in general, limited to the simulation of a finite number of electrons N under periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas at finite temperature, as it is relevant to contemporary research, e.g., in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor S(q) and in the interaction energy v, which is based on the density response formalism. We demonstrate that this method often allows us to obtain v in the thermodynamic limit within a relative accuracy of ∼0.2% from as few as N = 4 electrons without any empirical choices or knowledge of results for other values of N. Finally, we evaluate the applicability of our method upon increasing the density parameter rs and decreasing the temperature T.
The ideal Fermi gas in a finite volume is studied in the low-temperature regime where the thermal correlation length is comparable to the size L of the system. Physical quantities such as the density of fermions and the appropriate ordering susceptibility show oscillatory fluctuations around a smooth background as L is varied. These are investigated numerically and analytically. The amplitude of the fluctuations depends on the observable in question and on the container shape. Finite-size scaling does not hold directly for thermodynamic quantities but is recoverable by averaging the mean-squared fluctuations over an appropriate range in L.
We calculate the momentum distribution of the Fermi-liquid phase of the homogeneous two-dimensional electron gas. We show that close to the Fermi surface, the momentum distribution of a finite system with NNN electrons approaches its thermodynamic limit slowly, with leading-order corrections scaling as ${N}^{\ensuremath{-}1/4}$. These corrections dominate the extrapolation of the renormalization factor ZZZ and the single-particle effective mass ${m}^{\ensuremath{\ast}}$ to the infinite system size. We show how convergence can be improved using analytical corrections. In the range $1\ensuremath{\le}{r}_{s}\ensuremath{\le}10$, we get a lower renormalization factor ZZZ and a higher effective mass ${m}^{\ensuremath{\ast}}>m$ compared to the perturbative random-phase approximation values.