Low-lying excitations in a strongly interacting Fermi gas

Ruwan Senaratne, Danyel Cavazos-Cavazos, Ya-Ting Chang +1 more

A. P. Protogenov

Prof Michele Fabrizio

A central problem in the theory of strongly correlated fermion systems, concerns the nature of their low-lying excitations. It is generally accepted that, except for special cases with symmetry breaking, three dimensional (3D) interacting Fermi systems, are well described in terms of weakly correlated quasi-particles with quantum numbers in one-toone correspondence with those identifying the excitations of a non-interacting Fermi gas. This is the basic assumption underlying the Landau theory of Fermi liquids (FL), which was originally proposed as a phenomenological description of strongly interacting fermions by Landau in early 1956[1), an then established microscopically by Nozieres and Luttinger in 1962[2]. Quite a different scenario occurs in lD interacting Fermi systems. Apart from specific models developing gaps in the excitation spectrum, most fermion systems in one dimension with repulsive interactions, do have low-lying gapless excitations, like ordinary Fermi liquids, but totally different from the quasi-particles predicted by Landau theory. The low-energy behavior of most of these lD interacting fermion systems with gapless linear excitations, can be understood in terms of few model dependent constants, which parametrize all the long-wavelength properties...

Anna Minguzzi, Patrizia Vignolo, M. L. Chiofalo +1 more

We consider a time-dependent nonlinear Schr\"odinger equation in one dimension (1D) with a fifth-order interaction term and external harmonic confinement, as a model for both (i) a Bose gas with hard-core contact interactions in the local-density approximation, and (ii) a spin-polarized Fermi gas in the collisional regime. We evaluate analytically in the Thomas-Fermi limit the density fluctuation profiles and the collective excitation frequencies, and compare the results for the low-lying modes with those obtained from numerical solution of the Schr\"odinger equation. We find that the excitation frequencies are multiples of the harmonic-trap frequency even in the strong-coupling Thomas-Fermi regime. This result shows that the hydrodynamic and the collisionless collective spectra coincide in the harmonically confined 1D Fermi gas, as they do for sound waves in its homogeneous analog. It also shows that in this case the local-density theory reproduces the exact collective spectrum of the hard-core Bose gas under harmonic confinement.

John E. Thomas, S. L. Hemmer, Joseph M. Kinast +3 more

Seiji Yunoki

Low-lying one-particle anomalous excitations are studied for Gutzwiller-projected strongly correlated BCS states. It is found that the one-particle anomalous excitations are highly coherent, and the numerically calculated spectrum can be reproduced quantitatively by a renormalized BCS theory, thus strongly indicating that the nature of low-lying excitations described by the projected BCS states is essentially understood within a renormalized Bogoliubov quasiparticle picture. This finding resembles the well-known fact that a Gutzwiller-projected Fermi gas is a Fermi liquid. The present results are consistent with numerically exact calculations of the two-dimensional $t\text{\ensuremath{-}}J$ model as well as recent photoemission experiments on high-${T}_{\mathrm{C}}$ cuprate superconductors.