Multipartite states and Luttinger liquids of composite fermions
Sreejith Ganesh Jaya
Materials exhibiting exotic quantum phenomena at a macroscopic level are of great
interest because of its intrinsic value to Physics, and also because of its potential
applications in technology. Strongly correlated electronic systems form interesting
examples of these. Exploring them calls for a good understanding of its physics,
and development of new tools that are applicable to their analysis. Robustness
of the fractional quantum Hall effect (FQHE) makes it an ideal stage to study
strongly correlated electron systems. The complexity of the FQHE problem stems
directly from the strong interactions between the constituent particles and not
from the specific nature of the material it is implemented in. This work attempts
to gain a theoretical description of some of the less understood aspects of FQHE.
FQHE in the lowest Landau level is well understood using the theory of weakly
interacting emergent particles called composite fermions. Composite fermions
formed in the second Landau level however appear to be strongly interacting.
Of particular interest is the FQHE at 2 + 1/2 filling fraction, where the many body
ground state is believed to be described by a paired state of composite fermions,
represented by the Pfaffian wavefunction. Based on predicted properties of its
excitations, there has been proposals for implementing topological quantum com-
putations in this system. However a good understanding of the nature of these
excitations is still lacking.
This thesis introduces a class of many body wavefunctions called “bipartite
composite fermion states” that provide a unified description of all excitations of the
paired state at 5/2. In the bipartite composite fermion (BCF) picture, constituent
composite fermions split into two partitions which are correlated to each other.
Within each partition, they fill the lowest composite fermion Landau level of its
partition.
Properties of the BCF state can now be related to the properties of the individual partitions, which are well understood in terms of the composite fermion
theory. In particular, we show that the excitations of BCF states are obtained by
creating excitations in the individual partitions. The paired state with odd number of composite fermions should have an unpaired composite fermion. The BCF
model predicts that this unpaired composite fermion behaves as an exciton in the
quasiparticle and quasihole are in separate partitions. We confirm this prediction
numerically in finite size systems. Generalizations of bipartite composite fermion
functions to other filling fractions especially 2 + 4/7 and 2 + 3/5 are also studied.
Idea of bipartite composite fermions can be generalized to the case of more
partitions. Specifically, we look at tripartite composite fermion states which are
similar to the bipartite states, except that these have three correlated partitions
instead of two. Tripartite states have a filling fraction of ν = 3/5, and its particle
hole conjugate is a candidate wavefunction for describing the ν = 2 + 2/5…
•May 1, 2012•0 citations