Strong Fermion Interactions in Fractional Quantum Hall States : Correlation Functions

S. B. Mulay, John J. Quinn, Mark Shattuck

J. W. Kim, H. Kim, N. Kim

We apply Fermi hypernetted-chain theory to study the spin polarization of higher-order fractional quantum Hall (FQH) states at filling factors in between the primary FQH sequences, $\ensuremath{\nu}=p/({q}_{e}p\ifmmode\pm\else\textpm\fi{}1)$, where ${q}_{e}$ is an even integer and $p$ is a nonzero integer. The filling factors related to the higher-order FQH states include $\ensuremath{\nu}=3/8$, $4/11$, $5/13$, $5/17$, $4/13$, $6/17$, $7/11$, and so on. We use a model of strongly interacting fermions with different spin degrees of freedom to explain the states beyond primary FQH sequences. We calculate the correlation energy, the radial distribution function, as well as the static structure function associated with the Halperin wave function adopted for the mixture states of fermions with different spins. The results are comparable with those from the residual interaction between composite fermions.

Simon C. Davenport, Ivan Dario Jimenez Rodriguez, Johannes K. Slingerland +1 more

We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states---the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect---can be very well described in terms of a simple model of noninteracting (or weakly interacting) composite fermions.

Wade DeGottardi, Mohammad Hafezi

Bartosz Kuśmierz, Ying-Hai Wu, Arkadiusz Wójs

Fractional quantum Hall eect is a remarkable behaviour of correlated electrons, observed exclusively in two dimensions, at low temperatures, and in strong magnetic elds.The most prominent fractional quantum Hall state occurs at Landau level lling factor ν = 1/3 and it is described by the famous Laughlin wave function, which (apart from the trivial Gaussian factor) is an example of Jack polynomial.Fermionic Jack polynomials also describe another pair of candidate fractional quantum Hall states: MooreRead and ReadRezayi states, believed to form at the ν = 1/2 and 3/5 llings of the second Landau level, respectively.Bosonic Jacks on the other hand are candidates for certain correlated states of cold atoms.We examine here a continuous family of fermionic Jack polynomials whose special case is the Laughlin state as approximate wave functions for the 1/3 fractional quantum Hall eect.

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