Mean Field Description of the Fractional Quantum Hall Effect Near ν=1/(2k+1)\nu=1/(2k+1)

The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential $\mu_0$ and magnetic field $B$ corresponding to a ``special'' filling fraction $\nu=2\pi\rho/eB=1/n$ ($n=1,3,5\cdot \cdot\cdot$) we show that a deviation of $\mu$ in a finite range around $\mu_0$ does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on $\mu$ in a finite range about $\mu_0$ in this model. However when $\mu-\mu_0 \mu_{cr}^+$) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of $\mu$ and $\nu$ over which the system of vortices is dilute.Comment: Revtex document; 12 pages and 4 postscript figures in a fil

Quantum spin configurations in Tb2Ti2O7

Low energy collective angular momentum states of the Tb3+ ions in Tb2Ti2O7 are classified according to the irreducible representations of the octahedral point group. Degeneracy lifting due to the exchange interaction is discussed. Diffuse neutron scattering intensity patterns are calculated for each collective angular momentum state and the ground state is inferred by comparing to experiment.Comment: 5 pages, 1 colour figure. Slight corrections and additions to text and figur

Structural distortion and the spin liquid state in Tb2Ti2O7

It is shown that a k=0, A_{2u} distortion of the terbium tetrahedral network in Tb2Ti2O7 accounts for the apparent isolation of single tetrahedra as seen in neutron scattering studies. Single tetrahedron collective spin states, rather than individual spins, account for the main features of the spin liquid state, namely, fluctuating local moments and the absence of long range order. Singlet and doublet collective spin ground states are considered. An effective interaction between tetrahedra on the fcc lattice is derived and found to be weak and anisotropic.Comment: 5 page