  In one spatial dimension, anyons in the original description of Leinaas and
Myrheim are formally equivalent to locally interacting bosons described by the
Lieb-Liniger model. This admits an interesting reinterpretation of interacting
bosons in the context of anyons. We elaborate on this parallel, particularly
including the many-body bound states from the attractive Lieb-Liniger model. In
the anyonic context these bound states are created purely by
quantum-statistical attraction and coined quantum-statistical condensate, which
is more robust than the Bose-Einstein condensate. We introduce the second
quantization formalism for the present anyons and construct the generalized
Jordan-Wigner transformation that connects them to the bosons of the
Lieb-Liniger model.
