Master Degree Project Presentation: Geometric phases in the almost-bosonic anyon gas

Abstract: We study geometric phases arising in the almost-bosonic anyon gas, for which a two-parameter Chern-Simons-Schrödinger energy functional was previously derived. We found that the ground states of the model are well approximated by states of the nonlinear Landau levels (NLL), a family of explicit soliton solutions parametrised by coprime polynomials. Using these explicit states, we compute abelian Berry phases associated with adiabatic transport along closed loops in the parameter space given by vortex positions, scaling, and interaction terms. The Berry phase can be interpreted as the holonomy of the U(1)-connection for which we derive explicit integral formulas and evaluate them for several symmetric states. The results indicate a dependence of the Berry phase on the topology of the configuration space. Our work contributes to the understanding of geometric aspects of many-anyon systems and connects to holonomic quantum computation.