Quantum Monte Carlo for bosons

We will represent the inter-boson interaction by a pairwise, repulsive potential

$$ \begin{equation} V_{int}(|\mathbf{r}_i-\mathbf{r}_j|) = \Bigg\{ \begin{array}{ll} \infty & {|\mathbf{r}_i-\mathbf{r}_j|} \leq {a}\\ 0 & {|\mathbf{r}_i-\mathbf{r}_j|} > {a} \end{array} \tag{6} \end{equation} $$

where \( a \) is the so-called hard-core diameter of the bosons. Clearly, \( V_{int}(|\mathbf{r}_i-\mathbf{r}_j|) \) is zero if the bosons are separated by a distance \( |\mathbf{r}_i-\mathbf{r}_j| \) greater than \( a \) but infinite if they attempt to come within a distance \( |\mathbf{r}_i-\mathbf{r}_j| \leq a \).