Eur. Phys. J. B 61, 325-329 (2008)
https://doi.org/10.1140/epjb/e2008-00076-2

Interacting potential between spinons in the compact QED₃ description of the Heisenberg model

¹ Department of Physics and Institute for Basic Science Research, Sungkyunkwan University, Suwon, 440-746, Korea
² Laboratoire de Physique Théorique, Université Louis Pasteur, 67084 Strasbourg Cedex, France

Corresponding author: ^a rdillen@skku.edu

Received: 13 August 2007
Revised: 5 November 2007
Published online: 22 February 2008

Abstract

We implement a Chern-Simons (CS) contribution into the compact QED₃ description of the antiferromagnetic Heisenberg model in two dimensions at zero temperature. The CS term allows for the conservation of the SU(2) symmetry of the quantum spin system and fixes the flux through a plaquette to be a multiple of π as was shown by Marston. We work out the string tension of the confining potential which acts between the spinons and show that the CS term induces a screening effect on the magnetic field only. The confining potential between spinons is not affected by the CS flux. The strict site-occupation by a single spin 1/2 is enforced by the introduction of an imaginary chemical potential constraint.