Bosonization approach to charge and spin dynamics of 1D fermions with band-curvature

• Published in: arXiv.org 2007-05
• Main Author: Teber, Sofian
• Format: Article
• Language: English
• Subjects: Curvature; Decay; Excitation spectra; Fermions; Forward scattering; Quantum wires; Spin dynamics; Structure factor; Variation; Weight
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0609754

We consider one-dimensional (1D) spin-1/2 fermions in a clean quantum wire, with forward scattering interactions and a non-linear single-particle spectrum, \(\xi_k = v|k| + k^2/2m\) where \(v\) is the Fermi velocity and \(1/m\) is the band-curvature. We calculate the dynamical structure factor (DSF) of the model at small wave-vector \(q\) with the help of the bosonization technique. For spinless fermions, we show that, starting from the single-parametric spectrum: \(\om = u |q|\), bosonization emulates the 2-parametric excitation spectrum: \(\om = u |q| \pm q^2/2m^*\), where \(m^*\) decreases with increasing repulsive interactions. Moreover, away from the excitation-cone, {\it i.e.} \(\om \gg u |q|\), bosonization yields the 2-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band-curvature affects charge and spin DSF in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at \(\om = u_\rho |q|\) but also a spin peak at \(\om = u_\sigma |q|\), as charge fluctuations may decay via chargeless spin-singlet excitations. For the magnetic DSF, SCC manifests as a continuous transfer of magnetic spectral weight to frequencies \(\om > u_\sigma |q|\), as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.