The Effects of Dzyaloshinskii-Moriya Interactions on a Heisenberg Quantum Antiferromagnet on a Kagome Lattice: A Two-Singlet Schwinger-Boson, Mean-Field Analysis

Abstract

This thesis uses Schwinger-boson mean-field theory in the two-singlet formulation to analyze the effect of Dzyaloshinskii-Moriya interactions on a Heisenberg quantum antiferromagnet on the kagome lattice.The frustrated geometry of the kagome lattice makes it plausible that the ground-state is a spin-liquid. This has been supported by recent experiments, which makes it important to study such systems from the theoretical view. The analytical part of this thesis formulates the Heisenberg model with Dzyaloshinskii-Moriya interactions in a two-singlet Schwinger-boson scheme, makes the Hamiltonian quadratic trough a mean-field decoupling and diagonalizes it by Fourier and Bogoliubov transformations. The equations needed to find self-consistent values of the mean-field parameters are also derived. The numerical part solves the self-consistent equations numerically trough a iterative scheme.The numerical result are combined to form the T = 0 phase-diagram. This shows that the Dzyaloshinskii-Moriya interactions induces quantum phase-transitions between the different symmetric spin-liquid ansatzes considered. The phase-diagram reproduces the overall features found in earlier one-singlet calculations, but with the phaseboundaries shifted.