Figure 1

(Color online) (a) Pictorial view of the random singlet ground state. Bonds connecting spins denote singlet pairs. (b) The ground state from the point of view of the highlighted spin pair.Reuse & Permissions

Figure 2

(Color online) Normalized histogram of fidelities for those spin pairs separated by distances greater than a cutoff $l_c=L_0∕6$ for the disordered [$\alpha =0.3$, leftmost solid (black) and dashed (green) curves] and the clean and ordered chains [rightmost solid (orange) and dashed (purple) curves], and for length chains $L_0=100$ (solid lines) and $L_0=200$ (dashed lines). (a) The typical value of $F$ is clearly greater in the clean chain than in the disordered one. (b) However, as revealed by the logarithmic scale, there are some rare spin pairs (rare events) displaying high fidelities in the disordered chain, while in the clean one the fidelities are sharply constrained to values less than 1/2. A total of 6000 different disordered chains were used to build each one of these histograms.Reuse & Permissions

Figure 3

(Color online) Fidelity distribution $Q\left(F\right)$ for the chains with disorder parameter (a) $\alpha =0$, (b) $\alpha =0.3$, and (c) $\alpha =0.6$, concerning the last decimated spin pairs separated by distances greater than $l_c=L_0∕6$. The same in panel (d) for a fixed length $L_0=200$ and different disorder parameters. Open (solid) symbols refer to spin pairs separated by distances greater (shorter) than $l_c$. The vertical dashed line highlights the threshold $F=1∕2$ below which there is no entanglement.Reuse & Permissions