Three M-Species Generalizations for Rotating Bose Gases in the Lowest Landau Level

Abstract

We generalize three known theoretical results from 1- and 2-species systems to an M-component rotating Bose gas in the lowest Landau level (LLL). First, we find a subspace of the Hilbert space which is closed under homogeneous interaction and diagonalize analytically within this subspace to find the eigenenergies. This is a straight-forward generalization of Ref. [1] from 2 to M species. Second, we state and prove the validity of a basis for a particular class of composite fermion (CF) trial wave functions, known as "simple states" [2], for M-component Bose gases. By doing so, we generalize the simple state basis for 2-component Bose gases found in Ref. [3]. The number of basis elements in the M -component basis is linked to a certain class of combinatorial polynomials called q-multinomials. The proof of the M-component basis has been condensed into an article [4] and is currently under consideration by Journal of Physics A. Third, we have developed numerical tools to study the properties of the CF formalism applied to M -species Bose gases in the LLL and show that the formalism is excellent in capturing the low-energy behavior of such systems for M > 2. This is a generalization of previous results [5, 6, 2], which has shown that the CF formalism is excellent when applied to 1- and 2-component Bose gases. As part of this third generalization, we show how the formalism of simple states captures a class of eigenfunctions of the homogeneous contact interaction. This can be used to effectively visualize the evolution of the ground state of N spin-1 bosons under spin-independent interaction as a function of angular momentum L (originally found in Ref. [7]) for L ≤ N .