Physical Review Letters

Flux-carrying fermions and the second virial coefficient

Thomas Blum, C. R. Hägen, S. Ramaswamy

Published Feb 12, 1990• 41 citations

Abstract

The second virial coefficient ${\mathrm{B}}_{2}$ 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 ${\mathrm{B}}_{2}$ when viewed as a function of the flux parameter \ensuremath{\alpha}, one obtains here the remarkable result that there exist discontinuities in ${\mathrm{B}}_{2}$ at all even, nonzero values of \ensuremath{\alpha}.

DOI: 10.1103/physrevlett.64.709

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Physical Review Letters

Flux-carrying fermions and the second virial coefficient

Thomas Blum, C. R. Hägen, S. Ramaswamy

Published Feb 12, 1990• 41 citations

Publisher

Abstract

The second virial coefficient

{\mathrm{B}}_{2}

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

{\mathrm{B}}_{2}

when viewed as a function of the flux parameter \ensuremath{\alpha}, one obtains here the remarkable result that there exist discontinuities in

{\mathrm{B}}_{2}

at all even, nonzero values of \ensuremath{\alpha}.

DOI: 10.1103/physrevlett.64.709

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The second virial coefficient

{\mathrm{B}}_{2}

{\mathrm{B}}_{2}

when viewed as a function of the flux parameter \ensuremath{\alpha}, one obtains here the remarkable result that there exist discontinuities in

{\mathrm{B}}_{2}

at all even, nonzero values of \ensuremath{\alpha}.

Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form

g/r^2 (g > 0)

. All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the

\\omega \\to 0

limit, where

\\omega

is a frequency of harmonic oscillator which is introduced as a regularization method. As

g

approaches to zero, the result reduces to the noninteracting hard-core limit.

We consider the statistical mechanics of an interacting anyon gas with a repulsive pair potential of the form g/

{\mathit{r}}^{2}

. The second virial coefficient is calculated and shown to be a smooth function of the statistical parameter \ensuremath{\alpha} for g>0, without the cusps previously found at the Bose point in a noninteracting anyon gas. As g\ensuremath{\rightarrow}0 the cusps remain absent but a different type of singularity develops at the Bose point, showing that the order of limits is crucial.

{\mathit{A}}_{3}

as a function of the flux strength \ensuremath{\alpha} (\ensuremath{\alpha}=0 for fermions, \ensuremath{\alpha}=1 for bosons) are reliable in the range 0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}0.25. $A sub 3--- increases quadratically with \ensuremath{\alpha} for very small \ensuremath{\alpha}, but higher powers contribute substantially for large \ensuremath{\alpha}.