Ground State for Fractional Quantum Hall Effect

Robert Galejs

Xiong-Jun Liu, Xin Liu, L. C. Kwek +1 more

We propose fractional spin hall effect (FSHE) by coupling pseudospin states of cold bosonic atoms to optical fields. The present scheme is an extension to interacting bosonic system of the recent work \cite{liu,zhu} on optically induced spin hall effect in non-interacting atomic system. The system has two different types of ground states. The 1st type of ground state is a 1/3-factor Laughlin function, and has the property of chiral - anti-chiral interchange antisymmetry, while the 2nd type is shown to be a 1/4-factor wave function with chiral - anti-chiral symmetry. The fractional statistics corresponding to the fractional spin Hall states are studied in detail, and are discovered to be different from that corresponding to the fractional quantum Hall (FQH) states. Therefore the present FSHE can be distinguished from FQH regime in the measurement.

Allan H. MacDonald

Lotfi Belkhir, Jainendra K. Jain

Motivated by the observation of fractional quantum Hall effect (FQHE) at filling factor \ensuremath{\nu}=2+1/2 by Willett et al., we investigate the nature of the spin-singlet FQHE at \ensuremath{\nu}=1/2. We show that a simple trial wave function for the \ensuremath{\nu}=1/2 state, proposed earlier by one of us, is the exact nondegenerate ground state of a hard-core interaction model, and provide numerical evidence that it is adiabatically connected to the true Coulomb ground state.

R. Morf

Xiong-Jun Liu, Xin Liu, L. C. Kwek +1 more

We propose fractional spin Hall effect (FSHE) by coupling pseudospin states of cold bosonic atoms to optical fields. The present scheme is an extension to interacting bosonic system of the recent work [X.-J. Liu, X. Liu, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. 98, 026602 (2007) and S.-L. Zhu, H. Fu, C.-J. Wu, S.-C. Zhang, and L.-M. Duan, Phys. Rev. Lett. 97, 240401 (2006)] on optically induced spin Hall effect in noninteracting atomic system. The system has two different types of ground states. The first type of ground state is a 1/3-factor Laughlin function and has the property of chiral-antichiral interchange antisymmetry, while the second type is shown to be a 1/4-factor wave function with chiral-antichiral symmetry. The fractional statistics corresponding to the fractional spin Hall states are studied in detail and are discovered to be different from that corresponding to the fractional quantum Hall (FQH) states. Therefore the present FSHE can be distinguished from FQH regime in the measurement.