Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings

We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $\nu=2/3$, 4/5 and 4/3, and spin-partially-polarized states at filling factors 3/4 and 3/2, where "spin" serves as a generic label for the two components. We study ground states, excitations, edge states and entanglement spectrum for systems with up to 16 bosons, and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $\nu=2/3$, 4/5 and 3/4, although it is less satisfactory for the $\nu=3/2$ state. For $\nu=4/3$ a "non-Abelian spin-singlet" state has been proposed to occur for a 2-body contact interaction; we find that it is more likely that the actual state here is a spin-singlet state of reverse-flux-attached composite fermions at filling $\nu^*=4$. We also consider incompressible states at integral filling factors $\nu=1$ and 2. The incompressible state at $\nu=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\nu=2$ as the spin-singlet state of reverse-flux-attached composite fermions at $\nu^*=2$.