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

Physical review. B, Condensed matter

Density response of one-, two-, and three-dimensional fermion systems with repulsive δ -function interaction

Seido Nagano, K. S. Singwi

Published Dec 1, 1983• 3 citations
Publisher

Abstract

A closed-form formula for the density-density response function of a system of fermions interacting via a repulsive $\ensuremath{\delta}$-function potential in one, two, and three dimensions is given in an approximation in which the particle-hole interaction in the polarization bubble is considered to all orders. The dynamic and static structure factors and the local-field factor have been calculated.

DOI
10.1103/physrevb.28.6286

Related papers

Ground-state energy and density response of a one-dimensional fermion system with repulsive δ -function interaction

Seido Nagano, K. S. Singwi

The ground-state energy of a one-dimensional fermion system interacting via a repulsive $\ensuremath{\delta}$-function potential is calculated rigorously within the "ladder" approximation as a function of the coupling constant and the results compared with those given by the exact solution of Yang. Comparison with other many-body approximate theories has also been made. The density-density response function has also been calculated in an approximation in which the particle-hole interaction in the polarization bubble is taken into account to all orders. Results of this dynamic theory are compared with those of other approximations.

Physical review. B, Condensed matter•Jun 1, 1983•30 citations

Interacting Fermions in One Dimension. I. Repulsive Potential

James McGuire

The exact energies and wavefunctions for the ground state and low-lying excited states of a system of N − 1 one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large-volume, finite-density limit when the particles interact via a repulsive delta function potential. A number of properties of the system such as pair correlation functions and the effective mass of a certain class of excitations are also discussed.

Journal of Mathematical Physics•Mar 1, 1965•220 citations

Dynamical density and spin response functions of two-dimensional correlated fermion systems: Self-consistent second-order perturbation theory

A. Kotani, Dai S. Hirashima

Dynamical density and spin responses of a two-dimensional fermion system are studied with the self-consistent second-order perturbation theory using a model Hamiltonian. Special attention is paid to the density response at a large wave vector, where it was reported that a sharp mode develops below the particle-hole continuum in two-dimensional liquid ${}^{3}$He. We find that at a large wave vector, a peak in the dynamical density structure factor shifts to lower energy as interaction sets in, but it is not sharp enough to represent a well-defined mode because of the strong damping effect of the quasiparticles. We point out that it is necessary to treat the large damping effect properly in explaining the propagating mode found in two-dimensional liquid ${}^{3}$He.

Physical Review B•Jul 30, 2013•0 citations

Lindhard function of a d-dimensional Fermi gas

Bogdan Mihaila

We review in detail the derivation of the dielectric response function of a noninteracting system of spin-1/2 fermions in the random-phase approximation. Results for the response function of a Fermi gas in one, two and three dimensions can be obtained in closed form, and represent the baseline for developing a pedagogical understanding of the effect of correlations on the response functions in interacting systems of fermions.

arXiv:1111.5337•Nov 2, 2011•16 citations

Interacting Fermions in One Dimension. II. Attractive Potential

James McGuire

The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.

Journal of Mathematical Physics•Jan 1, 1966•160 citations

Polarized fermions in one dimension: Density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

Andrew C. Loheac, Jens Braun, Joaquín E. Drut

We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To that end, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.

arXiv:1804.10257•Physical review. D/Physical review. D.•Sep 11, 2018•20 citations
A closed-form formula for the density-density response function of a system of fermions interacting via a repulsive \ensuremathδ\ensuremath{\delta}\ensuremathδ-function potential in one, two, and three dimensions is given in an approximation in which the particle-hole interaction in the polarization bubble is considered to all orders. The dynamic and static structure factors and the local-field factor have been calculated.
The ground-state energy of a one-dimensional fermion system interacting via a repulsive $\ensuremath{\delta}$-function potential is calculated rigorously within the "ladder" approximation as a function of the coupling constant and the results compared with those given by the exact solution of Yang. Comparison with other many-body approximate theories has also been made. The density-density response function has also been calculated in an approximation in which the particle-hole interaction in the polarization bubble is taken into account to all orders. Results of this dynamic theory are compared with those of other approximations.
Dynamical density and spin responses of a two-dimensional fermion system are studied with the self-consistent second-order perturbation theory using a model Hamiltonian. Special attention is paid to the density response at a large wave vector, where it was reported that a sharp mode develops below the particle-hole continuum in two-dimensional liquid 3{}^{3}3He. We find that at a large wave vector, a peak in the dynamical density structure factor shifts to lower energy as interaction sets in, but it is not sharp enough to represent a well-defined mode because of the strong damping effect of the quasiparticles. We point out that it is necessary to treat the large damping effect properly in explaining the propagating mode found in two-dimensional liquid 3{}^{3}3He.
The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.
We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To that end, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.