Figure 1

The EE of a two-particle state $|k_1,k_2\rangle$ of a clean system as function of region $A$'s size $x=N_A/N$ for a system of length $N=1000$. The heavy lines correspond to the analytic prediction [dotted for $k_2-k_1=1$, Eq. (15), dashed for $k_2-k_1\gg 1$, Eq. (14)]. The thin lines pertain to the numerically calculated EE for all values of $k_2-k_1$ between 1 and 30, where odd values are depicted by red curves, and even ones by red curves. It is clear that for $k_2-k_1$ larger than 5 the numerical curves fit Eq. (14) quite well. It is also clear that all even $k_2-k_1$ reach the same EE value $S_A(x=1/2)=\ln \left(4\right)$ once $N_A=N/2$.Reuse & Permissions

Figure 2

The EE of 31 states of a clean system as function of region $A$'s size $N_A$ for a system of length $N=100$, in the absence ($U=0$, black line) or presence ($U=1$, dotted red line) of electron-electron interactions. Panel (a) depicts states in the vicinity of the ground state (the ground state and 1st–30th excitation), panel (b) shows the excitations around quarter of the two-particle band (1222th–1252st excitation). The heavy dashed line corresponds to the analytic prediction for $k_2-k_1\gg 1$, Eq. (14). For a clean system the interaction has no influence on the EE.Reuse & Permissions

Figure 3

The median EE of an ensemble of states for different regions of the band collected from 20 different realizations of strong disordered ($W=3$), as a function of region $A$'s size $N_A$ for a system of length $N=100$. Continuous lines depict the median EE in the vicinity of the ground state (1st–30th excitation), dotted lines at $a$$1/16$ of the band (294th–324th excitation), dashed lines at $a$$1/8$ of the band (603th–633th excitation), and dot-dashed lines at $a$$1/4$ of the band (1222th–1252th excitation). Black lines correspond to no electron-electron interactions, while red lines indicate the presence of moderate electron-electron interactions ($U=1$), and green lines correspond to stronger interactions ($U=3$). The heavy dashed line corresponds to the maximum EE for a clean system [Eq. (14)]. Error bars represent a range between the 40th and 60th percentiles.Reuse & Permissions

Figure 4

As in Fig. 3 for weak disordered ($W=1$). For high enough excitation energy, the median EE in the presence of disorder and interactions exceeds the maximum clean value indicated by the heavy dashed line [Eq. (14)].Reuse & Permissions