Quantum Hall States and Boson Triplet Condensate for Rotating Spin-1 Bosons

We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled $\mathrm{S}\mathrm{U}(4{)}_k$] includes the exact ground states of a model Hamiltonian at large angular momentum $L$, and also for $N=3k$ particles at $L=N$. The latter is a spin-singlet boson-triplet condensate. The second series, labeled $\mathrm{S}\mathrm{O}(5{)}_k$, includes exact ground states at large $L$ for different parameter values.

Figure 1

Overview of $c_0\mathrm{\text{−}}{c}_2$ plane, with special regions and directions marked.

Figure 2

Density profiles versus $x$ at $y=0$ in the LLL model: BTC (solid line); nonrotating BEC (broken line). Vertical axis is in units of the particle number $N=3p$.

Figure 3

GS values for $L$ as a function of the rotation frequency $\omega$ for $N=6$ particles at $c_2=0$. [We put ${\omega }_0=1$ and $c_0=(2\pi {)}^{3/2}/4$.] The state at $L=6$ is the BTC, while the $L=18$ state is the $\mathrm{S}\mathrm{U}(4{)}_1$ state. The spin values $S$ are shown for each GS.