Interactions in one dimension studied using the density matrix renormalization group

Abstract

In this dissertation, a density matrix renormalisation group program is developed, which is detailed and benchmarked for a spin chain with a Josephson junction. This program is then used to study interactions in a one-dimensional wire consisting of spinless, p-wave paired superconducting electrons. We study the effect that interactions have on the 4π Josephson effect by considering the degeneracies in the first few eigenstates of the Hamiltonian. It is found that the 4π Josephson effect is preserved up to finite size corrections, which indicates that particle hole symmetric interactions are not a source of quasiparticle poisoning. However, the finite size corrections decay slower than predicted by a non-interacting theory of the system with the same size gap. Thus, interactions affect the superconductivity in a way that is not accurately accounted for by an effective mean field theory