Licentiate Thesis: On the Rank of the Reduced Density Operator for the Laughlin State and Symmetric Polynomials
by
Babak Majidzadeh Garjani(Stockholm University, Department of Physics)
→
Europe/Stockholm
C5:1007
C5:1007
Description
One effective tool to probe a system revealing topological order is to bipartition the system in
some way and look at the properties of the reduced density operator corresponding to one part
of the system. In this thesis we focus on a bipartition scheme known as the particle cut in
which the particles in the system are divided into two groups and we look at the rank of the
reduced density operator. In the context of fractional quantum Hall physics it is conjectured
that the rank of the reduced density operator for a model Hamiltonian describing the system is
equal to the number of quasi-hole states. Here we consider the Laughlin wave function as the
model state for the system and try to put this conjecture on a firmer ground by trying to
determine the rank of the reduced density operator and calculating the number of quasi-hole
states. This is done by relating this conjecture to the mathematical properties of symmetric
polynomials and proving a theorem that enables us to find the lowest total degree of
symmetric polynomials that vanish under some specific transformation referred to as
clustering transformation.
