Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas

We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems.

Figure 1

A 1D array of particles carrying spin. The propagation of longitudinal (a) and transverse (b) spin waves over the fully polarized state $|\Uparrow ⟩$ is depicted. The state obtained by the action of the spin lowering operator $s_{-}(0,0)$ onto $|\Uparrow ⟩$ is schematically illustrated in (c).

Figure 2

Shown is the intensity plot of $t^{\alpha }\mathrm{Re}{G}_{\perp }(x,t)$ in the $x,t$ plane at $\gamma =100$. The spin wave is strongly suppressed at a distance $x\sim \ell (t)$, Eq. (16), long before it reaches the light cone, $x=vt$, shown as dashed green lines. The onset of the spin precession is seen in the space oscillations of $t^{\alpha }\mathrm{Re}{G}_{\perp }$ developing above the crossover time $t_{*}\simeq 15t_F$, shown by the white dotted line.