Master Defense

Alexander Hansen

Many-body Physics of Fock Parafermions - A Field Theoretical Approach Through Bosonisation

Research into the quasiparticles known as anyons has been an active branch of research ever since they where hypothesised to exist in two-dimensional materials in 1977. It was quickly shown that the modes of the fractional quantum Hall effect exhibit anyonic properties, when the effect was discovered experimentally in 1982. A quasiparticle called the parafermion, which first emerged in the area of condensed matter physics in the study of the vector Potts model,  displays anyonic properties by being Z_p-symmetric for some p in the integers. But what sets this class of quasiparticles aside, is that they are allowed to exist in spacial dimensions different from two. The exchange statistics of these parafermions make them very interesting to study from a theoretical standpoint. In 2014, it was furthermore shown that parafermions admit for a Fock space representation, which in turn permits these Fock parafermions to be described by particle number degrees of freedom. This realisation allows for the construction of Fock parafermions tight-binding models, which has been commenced to be studied over the last couple of years.
This thesis seeks to expand upon the literature by developing a field theoretical description of the general Z_p-symmetric Fock parafermions through bosonisation. Of special note is that the resulting description depends on (p-1) dual bosonic fields. The bosonisation description is applied to the tight-binding model of the Z_3-symmetric Fock parafermions for both single and pair-hopping terms, and it is shown how the model is a sum of a chiral Luttinger liquid and a Luttinger liquid up to second order. Furthermore, the two-point correlation functions of the Fock parafermions are calculated and it is shown that requiring the model to consist of (p-1) pairs of dual field renders the correct predictions of the two-point correlation functions as compared to earlier numerical calculations done by Rossini et al.

Zoom link: https://ucph-ku.zoom.us/s/66927054035