Bosonization approach to charge and spin dynamics of one-dimensional spin-1/2 fermions with band curvature in a clean quantum wire

We consider one-dimensional spin-1/2fermions in a clean quantum wire, with forward scattering interactions and a nonlinear 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 omega=u\q\, bosonization emulates the two-parametric excitation spectrum omega=u\q\+/- q(2)/2m(*), where m(*) decreases with increasing repulsive interactions. Moreover, away from the excitation cone, i.e., omega >> u\q\, bosonization yields the two-pair excitation continuum of the DSF. For spinful fermions, we show that the spin-charge coupling (SCC) due to band curvature affects the charge and spin DSFs in an asymmetric way. For the charge DSF, SCC manifests as a two-peak structure: a charge peak at omega=u(rho)\q\ but also a spin peak at omega=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 omega>u(sigma)\q\, as spin fluctuations decay via pairs of chargeless spin and spinless charge-neutral excitations.