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

TL;DR

This paper explores the properties of 1D anyons with two-body interactions, revealing a generalized Bose-Fermi mapping, distinct momentum distribution tails, and connections to Tan contacts and chiral symmetry breaking.

Contribution

It introduces a many-body Hamiltonian supporting bosonic and fermionic anyon states with a generalized mapping, extending known 1D zero-range interaction models.

Findings

Both bosonic and fermionic anyons exhibit $k^{-2}$ and $k^{-3}$ tails in momentum distribution.

The prefactors of the tails differ between bosonic and fermionic anyons.

Connections between exchange statistics, Tan contacts, and chiral symmetry breaking are established.

Abstract

Non-relativistic anyons in 1D possess generalized exchange statistics in which the exchange of two identical anyons generates a non-local phase that is governed by the spatial ordering of the particles and the statistical parameter $\alpha$. Working in the continuum, we demonstrate the existence of two distinct types of 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 $k^{-2}$ and $k^{-3}$ 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.