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arXiv:hep-th/9707109 · Journal of Physics A Mathematical and General

Screening in anyon gas

Subir Ghosh

Published Dec 21, 1997• 4 citations
arXivHTMLPDF

Abstract

Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern - Simons construction of anyons has helped considerably in computing the screening effect. Finally, the present model is compared with the conventional Chern - Simons construction.

DOI
10.1088/0305-4470/30/24/002

Related papers

Screening in Anyon Gas

Subir Ghosh

Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern-Simons construction of anyons has helped considerably in computing the screening effect. Finally the present model is compared with the conventional Chern-Simons construction. The possible existence of particles having arbitrary spin and statistics has been proved quite some time back [1, 2]. However, dynamical model building, on the other hand, has proved to be rather controversial, with the dispute still continuing. Basically there are two broad lines along which the models are conceived: (i) The Chern-Simons (CS) construction [3], where a point charge is coupled to CS eletrodynamics. Removal of the auxiliary (or statistical) CS gauge field renders the particle anyonic. (ii) The construction of minimal anyon field equations, where one starts from very general physical postulates, such as the mass shell and Pauli-Lubanski condition for the particle [4]. A variant of the latter scheme is the spinning particle model [5, 6, 7], with which we are concerned in the present Letter. The connection between the latter two is elaborated in [8].

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Abstract It is pointed out that Chern-Simons field theories do not always allow an interpretation in terms of anyons even in the nonrelativistic limit. Significantly, when the two approaches are found to differ the former is the one which is compatible with established physical principles. Thus the role left for the anyon is that of a very special subcase of Chern-Simons theories in the limit in which relativistic and spin considerations become irrelevant.

Zeitschrift für Naturforschung A•Feb 1, 1997•1 citation
Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern - Simons construction of anyons has helped considerably in computing the screening effect. Finally, the present model is compared with the conventional Chern - Simons construction.
Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern-Simons construction of anyons has helped considerably in computing the screening effect. Finally the present model is compared with the conventional Chern-Simons construction. The possible existence of particles having arbitrary spin and statistics has been proved quite some time back [1, 2]. However, dynamical model building, on the other hand, has proved to be rather controversial, with the dispute still continuing. Basically there are two broad lines along which the models are conceived: (i) The Chern-Simons (CS) construction [3], where a point charge is coupled to CS eletrodynamics. Removal of the auxiliary (or statistical) CS gauge field renders the particle anyonic. (ii) The construction of minimal anyon field equations, where one starts from very general physical postulates, such as the mass shell and Pauli-Lubanski condition for the particle [4]. A variant of the latter scheme is the spinning particle model [5, 6, 7], with which we are concerned in the present Letter. The connection between the latter two is elaborated in [8].
In this paper, we first briefly introduce a two-component anyon model and present unusual commutation relations between the two components. In the Fermi (or Bose) representation, drawing an electrostatic-field analogy, we found that the three-body interaction between particles can be approximately reduced to a logarithmic interaction. In the random-phase approximation, we calculated the effective interaction and dielectric response function. The effect of screening is to make the effective interaction nonsingular at q=0 and to induce a current-current interaction that does not appear in the original interaction. Finally, we found that there exists a restricted class of plasma excitations in the long-wavelength case.
I consider a gas of ``free'' anyons with statistical parameter \ensuremath{\delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling \ensuremath{\theta}=1/2\ensuremath{\delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field \ensuremath{\rho}/\ensuremath{\theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If \ensuremath{\delta}=\ensuremath{\pi}/m and the density \ensuremath{\rho}=r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If q is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of \ensuremath{\rho} and \ensuremath{\delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.
We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.