A Bosonic Model of Hole Pairs

We numerically investigate a bosonic representation for hole pairs on a two-leg t-J ladder where hard core bosons on a chain represent the hole pairs on the ladder. The interaction between hole pairs is obtained by fitting the density profile obtained with the effective model to the one obtained with the \tj model, taking into account the inner structure of the hole pair given by the hole-hole correlation function. For these interactions we calculate the Luttinger liquid parameter, which takes the universal value $K_{\rho}=1$ as half filling is approached, for values of the rung exchange $J'$ between strong coupling and the isotropic case. The long distance behavior of the hole-hole correlation function is also investigated. Starting from large $J'$, the correlation length first increases as expected, but diminishes significantly as $J'$ is reduced and bound holes sit mainly on adjacent rungs. As the isotropic case is approached, the correlation length increases again. This effect is related to the different kind of bonds in the region between the two holes of a hole pair when they move apart.Comment: 11 page

Mixed States of Composite Fermions Carrying Two and Four Vortices

There now exists preliminary experimental evidence for some fractions, such as $\nu$ = 4/11 and 5/13, that do not belong to any of the sequences $\nu=n/(2pn\pm 1)$, $p$ and $n$ being integers. We propose that these states are mixed states of composite fermions of different flavors, for example, composite fermions carrying two and four vortices. We also obtain an estimate of the lowest-excitation dispersion curve as well as the transport gap; the gaps for 4/11 are smaller than those for 1/3 by approximately a factor of 50.Comment: Accepted for PRB rapid communication (scheduled to appear in Nov 15, 2000 issue

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like $\Lambda$ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called "magnetoroton" minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B {\bf 48}, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar \emph{et al.} [Phys. Rev. Lett. {\bf 117}, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence $s/(2s+1)$ and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar \emph{et al.}'s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar \emph{et al.}'s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence $s/(2s\pm 1)$ in the lowest Landau level and the $n=1$ Landau level of graphene.Comment: 9 pages, 5 figures, published versio