Revisiting the Existence of Anyons

Ijaz Durrani

Stefan V. Mashkevich, Jan Myrheim, Kåre Olaussen

Yoshiki Fukusumi

In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can be summarized as the correspondence between conformal field theory and topological quantum field theory, but the latter has captured attention more recently because it suggests that one can deform the theories from one to another condensable or Witt equivalent. We reinterpret this phenomenon as the appearance of integrable flow at the edges of a topologically ordered system. By revisiting the existing phenomena from this view, one can relate the anyon condensation to the existing formalism of integrable models and their renormalization group flow. Moreover, we observe the robustness of the bulk-edge correspondence even under the existence of irrelevant perturbations at the edges. This formulation can enable one to analyze edge modes at the level of quantum fluid (non-linear) dynamics, or mixed state topological order even in non-Hermitian systems. Moreover, especially in the study of a class of non-Hermitian systems, we show a fundamental necessity to revisit Rogers-Ramanujan type identities as an appearance of the hidden (fractional) supersymmetric model which has a close relation to string field theories. Our view can give a unified paradigm to study edge modes of topologically ordered systems at the level of their dynamics potentially in both Hermitian and non-Hermitian systems.

Diptiman Sen

K.-V. Pham, M. Gabay, Pascal Lederer

Schulz and Shastry recently introduced a new class of exactly solvable one-dimensional models with non-Fermi-liquid physics. First, we show that this behavior is caused by the existence of anyonic excitations ( i.e. states with non-trivial conformal spin) with charge [(δ)/(2π)], where δ is the phase shift of the potential. Since δ is an arbitrary real number, these anyons may therefore carry an irrational charge. Next, in view of this result we revisit the general classification of non-Fermi-liquid two-species gapless 1D models: while it is usually thought that c = 1 × c = 1 theories form a four-parameter space, we establish that the most general non-relativistic conformal field theory has ten parameters. This defines a single larger universality class with sub-manifolds associated with the standard Luttinger liquid (with spin-charge separation), and the Schulz-Shastry class of models.

Alexei Kitaev