String-Order in Multileg Kitaev-Heisenberg Ladders

Abstract

The Kitaev model has become a source of much excitement in the field of condensed matter. It is a two dimensional model of spins ½ on a honeycomb lattice with bond-dependent interactions. Its interesting properties include a quantum spin liquid ground state and anyonic excitations. These properties could lead to exciting applications in quantum computing if materials were found to behave similarly to the Kitaev model. Such materials have been found, however the Kitaev model is too simple to describe these materials and additional interactions must be considered. The Heisenberg interaction is one such additional interaction. As such, we can define the Kitaev-Heisenberg model by combining the Kitaev and Heisenberg interactions. We can now ask ourselves if the quantum spin liquid ground state and anyonic excitations still exist in the Kitaev-Heisenberg model. To answer this question, a non-local string order parameter has been defined which is non-zero inside the quantum spin liquid phase and zero outside of it. This string order parameter was shown to exist and survive the Heisenberg interaction on the 2-leg ladder. In this thesis, we look to expand this result to multileg ladders such as the 3-leg, 4-leg, and 5-leg ladders to see if the string order parameter survives in the Kitaev-Heisenberg model in 2 dimensions. Our results show that the string order parameter does exist in multileg ladders, however the phase space window in which it survives the Heisenberg interaction is narrower than in the 2-leg ladder.