Magnetism is an active area of research as it is believed to play an important role in the understanding of important materials like the cuprate superconductors and the more recently discovered iron pnictide/chalcogenide superconductors. Magnetism is also of fundamental interest as very little, and no systematics, is known about a class of magnets known as frustrated magnets. Frustration means here that it is impossible to satisfy energetically all the magnetic interactions in the material simultaneously. An example of this is magnetic moments with interactions that favor antiparallel alignment of neighboring moments that are located on the corners of a triangle.

This master project is a followup study on a recently developed theory framework for studying frustrated classical Heisenberg magnets (M. Schecter, O.F. Syljuasen, and J. Paaske, "Nematic Bond Theory of Heisenberg Helimagnets", Phys. Rev. Lett. 119, 157202, (2017).). This framework uses diagrammatic techniques from statistical field theory to arrive at a set of self-consistent approximate equations which are then solved numerically to give information about phases, phase transitions, their universality class and critical temperatures. An advantage with the method is that it also captures phase transitions that break lattice symmetries like nematic phases.

The concrete purpose of this master project is to extend the field theoretic formalism to quantum magnets.

The type of work in this project will be partly analytic; involving the use of Feynman diagrams , and numerical; solving the resulting equations on a computer.