Edge modes of topologically ordered systems as emergent integrable flows: Robustness of algebraic structures in nonlinear quantum fluid dynamics

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.