Spectral-edge mode in interacting one-dimensional systems

O. Tsyplyatyev, A. J. Schofield

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Abstract

A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyze short-range interactions between Fermi particles and between Bose particles (with and without spin) using Bethe-ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empirical model of a free, nonrelativistic particle with an effective mass identified at low energies as the bare electron mass renormalized by the dimensionless Luttinger parameter K (or Kσ for particles with spin). The relevance of the Luttinger parameters beyond the low-energy limit provides a more robust method for extracting them experimentally using a much wider range of data from the bottom of the one-dimensional band to the Fermi energy. The empirical model of the spectral edge mode complements the mobile impurity model to give a description of the excitations in proximity of the edge at arbitrary momenta in terms of only the low-energy parameters and the bare electron mass. Within such a framework, for example, exponents of the spectral function are expressed explicitly in terms of only a few Luttinger parameters.
Original languageEnglish
Article number014309
Number of pages9
JournalPhysical Review B
Volume90
Issue number1
DOIs
Publication statusPublished - 31 Jul 2014

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