  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.
