Ballistic propagation of a local impact in the one-dimensional XY model

Abstract

Light-cone-like propagation of information is a universal phenomenon of nonequilibrium dynamics of integrable spin systems. In this paper, we investigate propagation of a local impact in the one-dimensional XY model with the anisotropy γ in a magnetic field h by calculating the magnetization profile. Applying a local and instantaneous unitary operation to the ground state, which we refer to as the local-impact protocol, we numerically observe various types of light-cone-like propagation in the parameter region 0 ⩽ γ ⩽ 1 and 0 ⩽ h ⩽ 2 of the model. By combining numerical integration with an asymptotic analysis, we find the following: (i) for |h| ⩾ |1 − γ 2| except for the case on the line h = 1 with , a wave front propagates with the maximum group velocity of quasiparticles, except for the case γ = 1 and 0 < h < 1, in which there is no clear wave front; (ii) for |h| < |1 − γ 2| as well as on the line h = 1 with , a second wave front appears owing to multiple local extrema of the group velocity; (iii) for |h| = |1 − γ 2|, edges of the second wave front collapses at the origin, and as a result, the magnetization profile exhibits a ridge at the impacted site. Furthermore, we find by an asymptotic analysis that the height of the wave front decays in a power law in time t with various exponents depending on the model parameters: the wave fronts exhibit a power-law decay t −2/3 except for the line h = 1, on which the decay can be given by either ∼t −3/5 or ∼t −1; the ridge at the impacted site for |h| = |1 − γ 2| shows the decay t −1/2 as opposed to the decay t −1 in other cases.