#### Thomas Jackson

Title: "Projection Hamiltonians for clustered quantum Hall wavefunctions"

Abstract: One of the main measures for determining whether a trial wavefunction for the fractional quantum Hall effect is physically realistic is the properties of an associated projection Hamiltonian, an artificial few-body Hamiltonian constructed so that the given wavefunction and edge excitations lie in the zero-energy eigenspace. The results presented here address the general (and nontrivial) problem of finding a projection Hamiltonian for a quantum Hall state defined in terms of a conformal field theory.

We consider lowest Landau level wavefunctions for bosons subjected to a magnetic field in the plane; "clustered" wavefunctions are those which vanish when k+1 (but not necessarily k) particles are brought to the same point. We begin by studying the zero-energy eigenstates of a projection Hamiltonian which forbids three particles to come together with relative angular momentum less than six and, in addition, forbids one of two linearly-independent states of relative angular momentum six. The counting of edge excitations of this Hamiltonian agrees with the character formula for the N=1 superconformal Kac vacuum module at generic (i.e., irrational) central charge c, despite the fact that the densest (ground) state reproduces the appropriate superconformal amplitude for all c.

The irrationality of the edge theory implies that this Hamiltonian is gapless for all c. For particular c, we try to ``improve'' the Hamiltonian by adding additional terms (related to singular vectors in the modules), so as to obtain a rational theory. We consider specifically states whose wavefunctions are related to the M(3,p) series of Virasoro minimal models.

**Location:**
PCTS Seminar Room

**Date/Time: **09/27/10
at
1:15 pm
- 09/27/10
at
6:00 pm

**Category: **Condensed Matter Seminar

**Department: **Physics