%0 Journal Article
%T Hierarchy of modes in an interacting system
%A O. Tsyplyatyev
%A A. J. Schofield
%A Y. Jin
%A M. Moreno
%A W. K. Tan
%A C. J. B. Ford
%A J. P. Griffiths
%A I. Farrer
%A G. A. C. Jones
%A D. A. Ritchie
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevLett.114.196401
%X Studying interacting fermions in 1D at high energy, we find a hierarchy in the spectral weights of the excitations theoretically and we observe evidence for second-level excitations experimentally. Diagonalising a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.
%U http://arxiv.org/abs/1408.3007v1