Figure 4

Left panel: behavior of the Von Neumann entropy S(t) relative to a \(\ell =10\) interval after a ground state quench of r from 1 to \(-1\), for \(N=10^4\). The dark red, red and orange curves correspond to different values of \(\lambda\) (\(\lambda = 1.24\), \(\lambda = 0.028\), \(\lambda =0.0028\)), which in turn corresponds to have 1, 116 and 221 resonant modes respectively. All curves refer to the case \(\alpha = 0.5\). The dotted dark blue and blue curves correspond to the short-range counterpart (\(\alpha = \infty\)) of the \(\lambda = 0.028\), \(\lambda = 0.0028\) cases. Central panel: Behavior of S(t) in the single-resonance phase (red), characterized by periodic bursts, compared with the analytical prediction of Eq. (11) (dashed yellow line). Right panel: Production of entanglement for larger times in the multi-resonant phase, compared with the correspondent limiting value \(\bar{S}\) for the same quench in the short-range limit (\(\alpha \rightarrow \infty\)). See Methods section "Numerical methods" for a more detailed explanation of the numerical procedure.