Universal momentum tail of identical one-dimensional anyons with two-body interactions

Nonrelativistic anyons in one dimension possess generalized exchange statistics in which the exchange of two identical anyons generates a phase that is governed by the spatial ordering of the particles and the statistical parameter $\ensuremath{\alpha}$. Working in the continuum, we demonstrate the existence of two distinct types of one-dimensional (1D) anyons, namely, bosonic anyons and fermionic anyons. We identify a many-body Hamiltonian with additive two-body zero-range interactions that supports bosonic and fermionic anyon eigenstates, which are, for arbitrary interaction strength, related through a generalized bosonic-anyon--fermionic-anyon mapping, an extension of the celebrated Bose-Fermi mapping for zero-range interacting 1D systems. The momentum distributions of bosonic and fermionic anyons are distinct: while both feature ${k}^{\ensuremath{-}2}$ and ${k}^{\ensuremath{-}3}$ tails, the associated prefactors differ. Our work reveals intricate connections between the generalized exchange statistics, the universal two- and three-body Tan contacts of systems consisting of $N$ identical particles, and the emergence of statistics-induced chiral symmetry breaking.