Figure 6

Numerical solutions for large lattice in 2D. Calculations for $30\times 30$ sites. Upper panel: Probabilities to have zero (red) and two (green) particles on a lattice site. Middle panel: $〈{\hat{b}}_{\mu }^{†}{\hat{b}}_{\mu +{\mathbf{e}}_{1}s}〉$, $s=1,\dots ,29$. Red line $s=v_{max}t$, $v_{max}=3J$. Lower panel: $〈{\hat{b}}_{\mu }^{†}{\hat{b}}_{\mu +({\mathbf{e}}_1+{\mathbf{e}}_2)s}〉$, $s=1,\dots ,29$. Red line $s=\sqrt{2}{v}_{max}t$, $v_{max}=3J/\sqrt{2}$. ${\mathbf{e}}_1$ and ${\mathbf{e}}_2$ are unit vectors along the lattice axes.