Multi-vortex Bose-Einstein condensate: examining the role of interaction range using Gaussian potential

We present exact diagonalization study on a system of $10 \leq N \leq 24$ spinless bosons interacting via repulsive Gaussian potential, harmonically confined in $xy$-plane with an externally impressed rotation about the $z$-axis. The two-body interaction strength in the Gaussian potential is taken in the strongly interacting regime with values of interaction range in the regime $0\leq \sigma \leq 1$. The diagonalization of the $N$-body Hamiltonian matrix, in subspaces of total angular momentum in the regime $0\le L_{z} \le 4N$ corresponds to the filling fraction $\nu\lesssim 3.2$ is carried out to obtain the variationally exact ground-state wavefunction and the corresponding eigenvalue. It is found that an increase in interaction range $\sigma$ leads to (a) a systematic decrease in energy, (b) an increase in the critical angular velocity $\Omega_{c_{i}}$ of the $i${th} vortex state and (c) an increase in the largest eigenvalue $\lambda_{1}$, (condensate fraction), of one-particle reduced density matrix (OPRDM). The von Neumann entropy $S_{1}\left(L_{z},\sigma\right)$, quantifying the quantum entanglement between the particles in the many-body ground state, is largely found to decrease with increase in $\sigma$. Crossings in von Neumann entropy for several of the angular momentum states are observed with variation in $\sigma$. The response of the Bose-Einstein condensate to rotation is examined through $L_{z}\left(\sigma\right)-\Omega\left(\sigma\right)$ stability graph for several values of $\sigma$. A vortex state with larger plateau length on the $L_{z}-\Omega$ graph is considered to be more stable. The internal structure of the condensate, as depicted by the conditional probability distribution (CPD) in the body-fixed frame, exhibits characteristic features with interaction range $\sigma$. One such feature is the merging of the cores of the two-vortex state.