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:1105.2964 · Journal of Physics Conference Series

Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas

Markus Holzmann, B. Bernu, David M. Ceperley

Published Sep 16, 2011• 20 citations
arXivHTMLPDF

Abstract

We analyze the extrapolation to the thermodynamic limit of Fermi liquid properties of the homogeneous electron gas in two and three dimensions. Using field theory, we explicitly calculate finite-size effects of the total energy, the renormalization factor, and the effective mass at the Fermi surface within the random phase approximation (RPA) and discuss the validity for general metallic systems.

DOI
10.1088/1742-6596/321/1/012020

Related papers

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

Quantum Monte Carlo calculation of the Fermi liquid parameters of the two-dimensional homogeneous electron gas

N. D. Drummond, Richard J. Needs

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.

arXiv:1307.4009•Physical Review B•Jul 25, 2013•11 citations

Momentum Distribution of the Homogeneous Electron Gas

Markus Holzmann, B. Bernu, Carlo Pierleoni +4 more

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)≲10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.

arXiv:1105.2338•Physical Review Letters•Sep 8, 2011•73 citations

Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal

Chetan Nayak, Joseph Henry Laboratories, Frank A. Wilczek

We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction ν = 1/2. We give a more complete description of our somewhat unorthodox renormalization group transformation by relating both our field-theoretic approach to a direct mode elimination and our anisotropic scaling to the general problem of incorporating curvature of the Fermi surface. We derive physical consequences of the fixed point by showing how they follow from renormalization group equations for finite-size scaling, where the size may be set by the temperature or by the frequency of interest. In order fully to exploit this approach, it is necessary to take into account composite operators, including in some cases dangerous “irrelevant ” operators. We devote special attention to gauge invariance, both as a formal requirement and in its positive role providing Ward identities constraining the renormalization of composite operators. We emphasize that new considerations arise in describing properties of the physical electrons (as opposed to the quasiparticles.) We propose an experiment which, if feasible, will allow the most characteristic feature of our results, that is the divergence of the effective mass of the quasiparticle near the nominal Fermi surface, to be tested directly. Some comparison with other recent, related work is attempted. 2

•Jan 1, 1994•70 citations

Finite-size effects in aD-dimensional ideal Fermi gas

Guozhen Su, Congjie Ou, Qiuping Alexandre Wang +1 more

By using the Euler–MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D -dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.

Chinese Physics B•Dec 1, 2009•7 citations

The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime

Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam

Abstract We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of N fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\frac {1}{3}}$ . In the limit $N\rightarrow \infty $ , we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.

arXiv:2106.11161•Forum of Mathematics Pi•Jan 1, 2023•17 citations
We analyze the extrapolation to the thermodynamic limit of Fermi liquid properties of the homogeneous electron gas in two and three dimensions. Using field theory, we explicitly calculate finite-size effects of the total energy, the renormalization factor, and the effective mass at the Fermi surface within the random phase approximation (RPA) and discuss the validity for general metallic systems.
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.
Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.
We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)≲10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.
We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction ν = 1/2. We give a more complete description of our somewhat unorthodox renormalization group transformation by relating both our field-theoretic approach to a direct mode elimination and our anisotropic scaling to the general problem of incorporating curvature of the Fermi surface. We derive physical consequences of the fixed point by showing how they follow from renormalization group equations for finite-size scaling, where the size may be set by the temperature or by the frequency of interest. In order fully to exploit this approach, it is necessary to take into account composite operators, including in some cases dangerous “irrelevant ” operators. We devote special attention to gauge invariance, both as a formal requirement and in its positive role providing Ward identities constraining the renormalization of composite operators. We emphasize that new considerations arise in describing properties of the physical electrons (as opposed to the quasiparticles.) We propose an experiment which, if feasible, will allow the most characteristic feature of our results, that is the divergence of the effective mass of the quasiparticle near the nominal Fermi surface, to be tested directly. Some comparison with other recent, related work is attempted. 2
By using the Euler–MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D -dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.
Abstract We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of N fermions on a torus, interacting via a two-body repulsive potential proportional to N−13N^{-\frac {1}{3}}N−31​ . In the limit $N\rightarrow \infty $ , we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.