Abstract
Simon Trebst (Microsoft Research)
Collective states of interacting anyons: Things golden
Topological quantum liquids in two dimensions such as the fractional quantum Hall states harbor exotic quasiparticles which due to their unusual exchange statistics are referred to as anyons. In this talk I will discuss the rich physics arising in one-dimensional models of interacting anyons, and highlight some of our results in the context of both two-dimensional classical systems and one-dimensional quantum spin systems. In particular, I will introduce generalizations of quantum spin Hamiltonians to anyonic degrees of freedom, such as the Heisenberg model or the Majumdar-Ghosh Hamiltonian. For chains of interacting Fibonacci anyons the energetic competition of two- and three-anyon interactions gives rise to a rich phase diagram with multiple critical and gapped phases. For the critical phases and their endpoints I will use numerical results to establish descriptions in terms of two-dimensional conformal field theory, and shortly discuss exact analytical results. I will then highlight the role of an inherent topological symmetry in protecting the critical phases. Finally, I will address how some of these findings generalize to other species of non-Abelian anyons.