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Physical Review

Collective Modes of a Spin-Density-Wave Structure

G. Fano, G. Pizzichini

Published Aug 5, 1967• 4 citations
Publisher

Abstract

The collective modes of a spin-density-wave structure are investigated in a one-dimensional model of a Fermi gas. The equations of motion in the random-phase approximation are completely solved at zero temperature and for a $\ensuremath{\delta}$-function interaction. The spin-density-wave structure has been found to be stable if its wavelength is equal to its best variational value. The complete dependence of the energy $\ensuremath{\omega}(q)$ of the collective modes on the momentum $q$ is exhibited. A new result is found and proved rigorously: The energy $\ensuremath{\omega}(q)$ vanishes when $\frac{2\ensuremath{\pi}}{q}$ is equal to the wavelength of the spin-density wave.

DOI
10.1103/physrev.160.219

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Progress of Theoretical Physics•Nov 1, 1984•3 citations
The collective modes of a spin-density-wave structure are investigated in a one-dimensional model of a Fermi gas. The equations of motion in the random-phase approximation are completely solved at zero temperature and for a \ensuremathδ\ensuremath{\delta}\ensuremathδ-function interaction. The spin-density-wave structure has been found to be stable if its wavelength is equal to its best variational value. The complete dependence of the energy \ensuremathω(q)\ensuremath{\omega}(q)\ensuremathω(q) of the collective modes on the momentum qqq is exhibited. A new result is found and proved rigorously: The energy \ensuremathω(q)\ensuremath{\omega}(q)\ensuremathω(q) vanishes when 2\ensuremathπq\frac{2\ensuremath{\pi}}{q}q2\ensuremathπ​ is equal to the wavelength of the spin-density wave.
The one-dimensional Fermi gas with attractive \ensuremath{\delta} interaction is treated in the quasiparticle random-phase approximation at zero temperature. The collective modes are evaluated numerically in the high-density (weak-coupling) and in the low-density (strong-coupling) case. Whereas in the weak-coupling limit the ordinary (particle-hole) random-phase approximation is approached for low momenta, the collective mode in the strong-coupling limit reproduces the Bogoliubov mode for the weakly interacting gas of particle-particle pairs (bosons). We find a smooth evolution of the collective modes from weak to strong coupling. Analytical approximations for the dispersion relation in the long-wavelength limit are derived for both weak and strong coupling. \textcopyright{} 1996 The American Physical Society.
Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.
Abstract Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green’s functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.
In this paper, we have studied the one-dimensional Fermi gas with attractive δ interaction potential in the quasi-particle random phase approximation at zero temperature. Using the theoretical formalism of Alm and Schuck, we have studied the behavior of collective modes over the whole coupling regime from weak coupling (high density) to strong coupling (low density). We observe that in the weak- coupling limit particle-hole RPA is approached to low momenta and the collective mode in the strong coupling limit reproduces the Bogoliubov mode for the weakly interacting bosons.
We calculate the spin and density susceptibility of Weyl fermions with repulsive S-wave interaction in ultracold gases. Weyl fermions have a linear dispersion, which is qualitatively different from the parabolic dispersion of conventional materials. We find that there are different collective modes for the different strengths of repulsive interaction by solving the poles equations of the susceptibility in the random-phase approximation. In the long-wavelength limit, the sound velocity and the energy gaps vary with the different strengths of the interaction in the zero sound mode and the gapped modes, respectively. The particle–hole continuum is obtained as well, where the imaginary part of the susceptibility is nonzero.
We investigate collective modes of the incommensurate spin-density wave state for a one-dimensional two-band model within the random phase approximation. For this model, compact expressions of the two-particle Green functions can be obtained. Three types of collective modes are found; an amplitude mode, a phase mode in a real space (a sliding mode) and a phase mode in a spin space (a spin wave mode). The amplitude mode appears in the longitudinal susceptibility and the spin wave mode appears in the transverse susceptibility, but the sliding mode is found to have no contribution to the susceptibilityes. The amplitude mode has the same energy with the energy gap of single particle excitations, but if it is couplied with phonons, its frequency is lowered and it makes a mid-gap mode.