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 $|\mathbf{r}_i-\mathbf{r}_j| \leq a$.

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