Hierarchy of modes in an interacting one-dimensional system

Research output: Contribution to journalArticlepeer-review


  • Y Jin
  • WK Tan
  • CJB Ford
  • JP Griffiths
  • I Farrer
  • GAC Jones
  • DA Ritchie

External organisations

  • Cavendish Laboratory


Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R2/L2, where 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 renormalized 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 tunneling of electrons (fermions with spin) from or 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.


Original languageEnglish
Article number196401
Number of pages5
JournalPhysical Review Letters
Publication statusPublished - 11 May 2015