%0 Journal Article
%T Ground state and low-lying collective excitations of trapped three-boson system in quantum Hall regime
%A Mohd. Imran
%A M. A. H. Ahsan
%J Physics
%D 2015
%I arXiv
%X A rotating system of bosons interacting via repulsive finite-range Gaussian potential, harmonically confined in quasi-two-dimension is studied for its ground and low-lying excited states in weakly to strongly interacting regime. The Hamiltonian matrix for $N=3$ boson system is diagonalized in subspaces of quantized total angular momenta $0\le L \le 4N$ in beyond lowest Landau level approximation to obtain the ground and low-lying eigenstates. Our numerical results suggest that breathing modes with eigenenergy spacing of $2\hbar\omega_{\perp}$, known to exist in strictly 2D system with zero-range ($\delta$-function) interaction potential, may as well be anticipated to exist in quasi-2D system with finite-range Gaussian interaction potential. The von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates. In the rapidly rotating bosonic fractional quantum Hall regime with angular momenta $L=\frac{q}{2}N\left(N-1\right),~q=2,4,\dots$, we examine the strongly correlated ground state and the corresponding low-lying collective excitations including the breathing modes for their quantum as well as spatial order. The ground state in these angular momentum subspaces, is indeed found to exhibit the anticorrelation structure suggesting that it may variationally be well described by a Bose-Lauglin like state. We observe that the first breathing mode exhibits features similar to the Bose-Laughlin state in having the eigenenergy, the von Neumann entropy and the internal structure being independent of interaction for the three-boson system considered here. On the contrary, for the eigenstates lying between the Bose-Laughlin state and the first breathing mode, the values of eigenenergy, von Neumann entropy and the internal structure are found to vary with interaction.
%U http://arxiv.org/abs/1508.05030v1