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arXiv:hep-th/9709057

The Second Virial Coefficient of Spin-1/2 Anyon Systems

Sahng-Kyoon Yoo, D. K. Park

Published Sep 8, 1997• 0 citations
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Abstract

We calculate the second virial coefficient of spin-1/2 anyon gas in the various values of the self-adjoint extension parameter by incorporating the self-adjoint extension method into the Green's function formalism. Especially, the completely different cusp- and discontinuity-structures from the result of previous literature are obtained when the self-adjoint extension parameter goes to infinity. This is originated from the different condition for the occurrence of irregular states.

DOI
10.48550/arxiv.hep-th/9709057

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We calculate the second virial coefficient of spin-1/2 anyon gas in the various values of the self-adjoint extension parameter by incorporating the self-adjoint extension method into the Green's function formalism. Especially, the completely different cusp- and discontinuity-structures from the result of previous literature are obtained when the self-adjoint extension parameter goes to infinity. This is originated from the different condition for the occurrence of irregular states.
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The second virial coefficient B2{\mathrm{B}}_{2}B2​ for a system of spin-one-half flux-carrying fermions is computed. It is found that there arise significant differences from known results for the corresponding spinless system. Apart from the existence of cusps and a restricted periodicity of B2{\mathrm{B}}_{2}B2​ when viewed as a function of the flux parameter \ensuremath{\alpha}, one obtains here the remarkable result that there exist discontinuities in B2{\mathrm{B}}_{2}B2​ at all even, nonzero values of \ensuremath{\alpha}.
Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert}r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​\ensuremath{\Vert}), where r2{\mathit{r}}^{2}r2U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.