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Communications in Theoretical Physics

Limiting Case of 1D Delta Anyon Model

Ren-Gui Zhu, Wang An-Min

Published Dec 1, 2008• 3 citations
Publisher

Abstract

In order to analyze a limiting case of the 1D delta anyon model, the coupling strength of the δ interaction c is modified to become a function of the anyonic parameter κ. A pedagogic derivation of the solution for this modified model using the method of anyon-boson mapping plus Bethe ansatz is presented. The limiting case as κ → π and simultaneously c → 0, which was previously neglected, is analyzed. Some unexpected properties of this limiting case are discovered. The BAEs are compared with previous results.

DOI
10.1088/0253-6102/50/6/02

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In order to analyze a limiting case of the 1D delta anyon model, the coupling strength of the δ interaction c is modified to become a function of the anyonic parameter κ. A pedagogic derivation of the solution for this modified model using the method of anyon-boson mapping plus Bethe ansatz is presented. The limiting case as κ → π and simultaneously c → 0, which was previously neglected, is analyzed. Some unexpected properties of this limiting case are discovered. The BAEs are compared with previous results.
The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.
We propose an exactly solvable model of one-dimensional anyons with competing δ-function and derivative δ-function interaction potentials. The Bethe ansatz equations are derived in terms of the N -particle sector for the quantum anyonic field model of the generalized derivative nonlinear Schrödinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of δ-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles.