Spectral edge mode in interacting one-dimensional systems

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 analyse 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, non-relativistic particle with an effective mass identified at low energies as the bare electron mass renormalised by the dimensionless Luttinger parameter $K$ (or $K_{\sigma }$ 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 wide 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.

11 pages, 7 figures

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• Hierarchy of modes in an interacting system
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Nature of the many-body excitations in a quantum wire: theory and experiment
• Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor
• Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low dimensions
• Splitting of Fermi point of strongly interacting electrons in one dimension: A nonlinear effect of spin-charge separation
• Semiconductor nanodevices as a probe of strong electron correlations
• Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality
• Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D Regime
• Dominant end-tunneling effect in two distinct Luttinger liquids coexisting in one quantum wire