Density Excitation Spectrum of the One-Dimensional Fermi Gas

V. Ya. Krivnov, Alexander A. Ovchinnikov

Marian Apostol, A. Corciovei, S. Stoica

Abstract The collective excitations of the particle‐density fluctuations are studied in the one‐dimensional Fermi gas by means of the generator coordinate method. The dispersion relation are obtained both, for the forward and backward scattering interaction. It is shown that for repulsive interaction a gap occurs in the frequency of the backscattering excitations at wavevectors equal to twice the Fermi momentum.

P. Schlottmann

The energy spectrum of the one-dimensional electron gas, solved by Luther and Emery for a particular attractive interaction strength $U$ of the backward scattering across the Fermi surface, has been calculated for small deviations from this particular limit. The energy spectrum shows a gap at the Fermi energy, whose magnitude is very sensitive to the interaction $U$. The density of states shows a gap at zero temperature, which is smeared out by the quasiparticle lifetime for $T\ensuremath{\ne}0$.

H. U. Everts, Hermann Schulz

Alexander A. Ovchinnikov, Anton Vladimirovich Zabrodin

Victor Gurarie

We present a study of a gas of bosons confined in one dimension with Feshbach-resonant interactions, at zero temperature. Unlike the gas of one-dimensional bosons with non resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses additional features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this regime in detail due to the lack of the appropriate formalism.