Linear Flavour-Wave Theory of SU(N) Lattice Models with Arbitrary Irreducible Representations

This thesis explores various approaches of studying the long-range colour order of antiferromagnetic SU(N) Heisenberg models with the linear flavour-wave theory (LFWT). The LFWT is an extension of the well-known SU(2) spin-wave theory to SU(N), and this semi-classical method has been used to study SU(N) models with colour-ordered ground states in the fundamental irreducible representation (irrep). The aim of this thesis is to study various SU(N) Heisenberg models in different irreps and in various colour configurations, in part by extending the LFWT method to different irreps of SU(N).

This will be achieved by using three different methods all using different bosonic representations. First, the LFWT willbe performed using the multiboson method that introduces a boson for each state of a given irrep. Then, a different SU(3) bosonic representation first introduced by Mathur & Sen will be presented and used to perform the LFWT calculations. Finally, another way of applying the LFWT will be shown using the bosons first used by Read & Sachdev for SU(N) irreps with rectangular Young tableaux. The specific models that will be treated by these methods are the fully antisymmetric SU(N) models on the square, honeycomb, and triangular lattices with m>1 particles per site, as well as the bipartite SU(3) Heisenberg chain in the adjoint irrep to show how the LFWT can be used for mixed symmetries. The last chapter of the thesis will be dedicated to another problem related to the accidental line of zero modes in the harmonic spectrum of the antiferromagnetic SU(3) Heisenberg model on the square lattice with one particle per site in a three-sublattice order. The objective will be to try to lift the accidental zero modes in the spectrum.