FRACTIONAL QUANTUM HALL STATES AND WIGNER CRYSTAL OF QUASI-PARTICLES

By using a bosonic Chern-Simons gauge theory the ground state of the planar electron system is analyzed in the presence of an external magnetic field. The distinctive feature of our theory is that a renormalization counter term (\alpha\/M) \psi\4 which represents explicitly a hard-core condition plays important roles, where alpha and M are the statistics parameter and the mass of the electron. The following results are obtained systematically in the semiclassical approximation. When nu = 1 / k (k odd) with nu being the Landau level filling factor, the ground state is incompressible and described by the Laughlin wavefunction. On the other hand, when nu approximately 1 / k, the ground state is compressible and it is given by the Wigner crystal made of quasiholes (antivortices). The wavefunction of the Wigner crystal is also calculated, which is found to coincide with that of the Laughlin quasiholes. In these analyses the Coulomb interaction between electrons plays a crucial role.