Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model

TL;DR

This paper develops a second quantization framework for Leinaas-Myrheim anyons in one dimension, revealing their equivalence to Lieb-Liniger bosons and introducing a generalized Jordan-Wigner transformation.

Contribution

It introduces a second quantization formalism for 1D anyons and establishes a connection to the Lieb-Liniger model via a generalized Jordan-Wigner transformation.

Findings

Anyons are equivalent to Lieb-Liniger bosons in 1D.

Quantum-statistical attraction leads to bound states.

The formalism includes a robust quantum-statistical condensate.

Abstract

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.