Anomalous Magnetic Moment of Anyons in three dimensional CPN−1 Model

We calculate the anomalous magnetic moment of anyons in three dimensional CPN−1 model with a Chern-Simons term in various limits in 1/N expansion. We have found that for anyons of infinite mass the gyromagnetic ratio (g-factor) is 2 up to the next-to-leading order in 1/N . Our result supports a recent claim that the g-factor of nonrelativistic anyons is exactly two. We also found that for − 8 π < θ < 0, the electromagnetic interation between two identical aynons of large mass are attractive. PACS numbers: 13.40.Fn, 11.10.Lm, 11.15.Pg E-mail address: [email protected] E-mail address: [email protected] One of the peculiarities of planar physics is that there exists a particle of arbitrary spin, called anyon, since the rotation group in the two-dimensional space is U(1). In field theories, anyon can be realized by minimally coupling a boson or a fermion to Chern-Simons gauge fields[1]. Due to the coupling to the Chern-Simons gauge fields, the wave function of two identical particles gets an Aharonov-Bohm phase, 4π κ , where κ is the coefficient of the Chern-Simons term in the Lagrangian. Since the Aharonov-Bohm phase is interpreted as a statistical phase, the particle gets an induced spin, S = 1/κ. Anyon has been studied extensively because of its possible application to some of the planar condensed matter systems. It is found that anyon matter exhibits superconductivity[2] and describes quantum Hall system[3]. To study the many-body effects of anyons, one needs to find out how they interact with each other. Besides the statistical interaction due to the Chern-Simons fields, anyons may interact electro-magnetically. Especially, the interaction between its magnetic moment and electric charge can be very important since it may lead to a bound state of anyon and a magnetic flux tube[4], which is introduced by Jain[5] to describe fractional quantum Hall effect. Depending on the sign of the magnetic moment of anyon, the interaction of identical anyons could be attractive while the electric charge-charge interaction is always repulsive. Therefore, for a certain value of the coefficient of the Chern-Simons term, two identical anyons can form a bound state. Finding out the exact value of the magnetic moment of anyon is therefore of some importance. There have been several calculations on the magnetic moment of anyon. Chou et al. showed that the g-factor of nonrelativistic anyonic particles is exactly two [6]. Also, in field theoretical models, it is shown that in the pure anyonic limit (namely for large value of the coefficient of the Chern-Simons term) the gyromagnetic ratio of anyon at one-loop is g = 2+O (