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Chinese Physics B

Dispersion relation of excitation mode in strongly interacting fermions matter

Yanping Wang, Jisheng Chen

Published Dec 1, 2008• 6 citations
Publisher

Abstract

This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperature field theory. With the polarization tensor, the influences of temperature, particle number density and interaction strength on the dispersion relation are discussed in detail. It finds that the collective effects are qualitatively more important in the unitary fermions than those in the finite contact interaction matter.

DOI
10.1088/1674-1056/17/12/012

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This paper analyses the dispersion relation of the excitation mode in non-relativistic interacting fermion matter. The polarization tensor is calculated with the random phase approximation in terms of finite temperature field theory. With the polarization tensor, the influences of temperature, particle number density and interaction strength on the dispersion relation are discussed in detail. It finds that the collective effects are qualitatively more important in the unitary fermions than those in the finite contact interaction matter.
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We investigate collective excitations in a dipolar and non-dipolar Fermi gas mixture at zero temperature.We obtain the density-density correlation functions of the mixtures in the ring diagram approximation.We analyze the dispersion relation determined by the poles of the density-density correlation functions and find two different types of collective modes: the undamped zero sound and the overdamped modes.We show that the undamped zero sound mode exists only at long wavelengths and the speed of undamped zero sound varies with the propagation direction due to an anisotropy of the dipolar interaction between dipolar fermions.We also show that the decay rate of the overdamped mode decreases as the inter-particle interaction strength between dipolar and non-dipolar fermions increases and the overdamped mode is replaced by unstable one if the inter-particle interaction strength is much strong.
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 calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick's theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.
We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick’s theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.
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.