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

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

A. Kotani, Dai S. Hirashima

Published Jul 30, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.88.014529

Related papers

Density fluctuation spectrum of two-dimensional correlated fermion systems

A. Kotani, Dai S. Hirashima

Density fluctuation spectrum of two-dimensional fermions that interact with short-range repulsive interaction is calculated with the self-consistent perturbation theory. The spectrum extends beyond the particle-hole continuum band in the noninteracting case because of the multiparticle excitations. At a large wave vector, a peak develops in the spectrum near the lower threshold of the particle-hole continuum. These results are compared with the recent inelastic neutron scattering experiment on two-dimensional 3 He adsorbed on graphite.

Journal of Physics Conference Series•Dec 17, 2012•1 citation

Exact behavior of the density and spin susceptibilities of a Fermi liquid for large wave vectors: Derivation from diagrammatic many-body theory

Giovanni Vignale

The exact asymptotic behavior of the density and spin response functions of a uniform Fermi system for large wave vectors is derived from diagrammatic many-body theory. Various exact relationships between the self-energy, the particle-hole interaction, and the vertex corrections are derived for the first time and applied to this problem. The final results agree with those provided by the kinetic equation approach. Different behavior of the polarization potentials and local-field factors for interactions that decrease faster or slower than 1/${q}^{2}$ for large wave vector q, is pointed out.

Physical review. B, Condensed matter•Oct 1, 1988•23 citations

PAIR EXCITATIONS AND VERTEX CORRECTIONS IN FERMI FLUIDS AND THE DYNAMIC STRUCTURE FUNCTION OF TWO-DIMENSIONAL 3 He

Helga M. Böhm, Henri Godfrin, E. Krotscheck +3 more

We use the equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids to develop a theory of the excitation spectrum and the single–particle self energy in such systems. We present here the fully correlated equations and their approximate solutions for 3 He . Our theory has the following properties: It reduces to both, i) the "correlated" random–phase approximation (RPA) for strongly interacting fermions if the two–particle–two–hole correlations are ignored, and, ii) to the correlated Brillouin–Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two first energy–weighted sum rules, and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad–hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair–excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization.

International Journal of Modern Physics B•May 30, 2007•4 citations

Spin-Density Response Function in a 2D Electron System under a Magnetic Field

Kanako Yoshizawa, Natsuko Hirano, Kazuo Takayanagi

We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.

Physical Review Letters•Aug 8, 2003•4 citations

Non-Fermi-liquid behaviour in the weak-coupling approach to correlated fermions

Gudrun Schliecker, K -D Schotte, Berislav Horvatić +1 more

It has become easy to calculate numerically self-energy corrections in second-order perturbation theory. In order to find out its capabilities and limitations, we analyse the weak-coupling approach for a system of one-dimensional correlated fermions. We compare the self-energy contributions due to different scattering processes of left- and right-moving particles which can be treated analytically. We find that for Tomonaga-Luttinger processes second-order perturbation theory gives reliable results and show how deviations from Fermi-liquid behaviour and the separation of spin- and charge-density excitations can be detected from the numerical data. Choosing the Hubbard model as a typical example we present numerical results for the self-energy and the spectral density. Special attention is paid to the case without particle-hole symmetry. The insulating behaviour at half filling is outside the scope of the weak-coupling method applied.

Journal of Physics Condensed Matter•Oct 9, 1995•0 citations

Fluctuation effects at the onset of 2kF density wave order with two pairs of hot spots in two-dimensional metals

Jáchym Sýkora, Walter Metzner

We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting ($2{k}_{F}$) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the $2{k}_{F}$ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.

arXiv:2104.11382•Physical review. B./Physical review. B•Sep 15, 2021•5 citations
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.
Density fluctuation spectrum of two-dimensional fermions that interact with short-range repulsive interaction is calculated with the self-consistent perturbation theory. The spectrum extends beyond the particle-hole continuum band in the noninteracting case because of the multiparticle excitations. At a large wave vector, a peak develops in the spectrum near the lower threshold of the particle-hole continuum. These results are compared with the recent inelastic neutron scattering experiment on two-dimensional 3 He adsorbed on graphite.
The exact asymptotic behavior of the density and spin response functions of a uniform Fermi system for large wave vectors is derived from diagrammatic many-body theory. Various exact relationships between the self-energy, the particle-hole interaction, and the vertex corrections are derived for the first time and applied to this problem. The final results agree with those provided by the kinetic equation approach. Different behavior of the polarization potentials and local-field factors for interactions that decrease faster or slower than 1/q2{q}^{2}q2 for large wave vector q, is pointed out.
We use the equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids to develop a theory of the excitation spectrum and the single–particle self energy in such systems. We present here the fully correlated equations and their approximate solutions for 3 He . Our theory has the following properties: It reduces to both, i) the "correlated" random–phase approximation (RPA) for strongly interacting fermions if the two–particle–two–hole correlations are ignored, and, ii) to the correlated Brillouin–Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two first energy–weighted sum rules, and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad–hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair–excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization.
We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.
It has become easy to calculate numerically self-energy corrections in second-order perturbation theory. In order to find out its capabilities and limitations, we analyse the weak-coupling approach for a system of one-dimensional correlated fermions. We compare the self-energy contributions due to different scattering processes of left- and right-moving particles which can be treated analytically. We find that for Tomonaga-Luttinger processes second-order perturbation theory gives reliable results and show how deviations from Fermi-liquid behaviour and the separation of spin- and charge-density excitations can be detected from the numerical data. Choosing the Hubbard model as a typical example we present numerical results for the self-energy and the spectral density. Special attention is paid to the case without particle-hole symmetry. The insulating behaviour at half filling is outside the scope of the weak-coupling method applied.
We analyze quantum fluctuation effects at the onset of charge or spin-density wave order in two-dimensional metals with an incommensurate nesting (2kF2{k}_{F}2kF​) wave vector connecting two pairs of hot spots on the Fermi surface. We first compute the momentum and frequency dependence of the fermion self-energy near the hot spots to leading order in a perturbation expansion (one loop). Non-Fermi liquid behavior with a linear (in energy) quasiparticle decay rate and a logarithmically vanishing quasiparticle weight is obtained. The momentum dependence of the self-energy entails only finite renormalizations of the Fermi velocity and the Fermi-surface curvature at the hot spots. The perturbative one-loop result is not self-consistent and casts doubt on the stability of the 2kF2{k}_{F}2kF​ quantum critical point. We construct a self-consistent solution of the one-loop equations with self-energy feedback, where the quantum critical point is stabilized rather than being destroyed by fluctuations, while the non-Fermi liquid behavior as found in the perturbative one-loop calculation is confirmed.