We study bilayer Fractional Quantum Hall State also known as Halperin state. We prove that for any filling fractions (positive rational numbers), there are infinite solutions that imply that infinite topological states are corresponding to any given filling fraction. Our results can apply to any charge vectors.
@article{arxiv.2004.09035,
title = {Halperin states can produce any filling fractions},
author = {En-Jui Kuo},
journal= {arXiv preprint arXiv:2004.09035},
year = {2020}
}