Thursday, March 21, 2013

1303.4716 (T. S. Jackson et al.)

Entanglement subspaces, trial wavefunctions, and special Hamiltonians in
the fractional quantum Hall effect

T. S. Jackson, N. Read, S. H. Simon
We consider systems of trial wavefunctions in the fractional quantum Hall effect that can be obtained in various ways. In one way, the functions are obtained by analyzing the entanglement of the ground state wavefunction, partitioned into two parts. In another, functions are defined by the way in which they vanish as several coordinates approach the same value, or by a projection operator Hamiltonian that enforces those conditions. In a third way, the functions are given by conformal blocks from a conformal field theory (CFT). These different sets are closely related. The use of CFT methods permits an algebraic formulation to be given for all of them. In some cases, we can prove that all of these spaces are the same (a finite-size bulk-edge correspondence), thus answering several questions and conjectures. We can also use the analysis of functions to produce a projection operator Hamiltonian that produces them as zero-energy states. For a model related to the N=1 superconformal algebra, the corresponding Hamiltonian imposes vanishing properties involving only three particles; for this we determine all the wavefunctions explicitly. We do the same for a sequence of models involving the M(3,p) Virasoro minimal models that has been considered previously, using results from the literature. We exhibit the Hamiltonians for the first few cases of these.
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