Approximate ground state of a confined Coulomb anyon gas in an external magnetic field

We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics $\ensuremath{\nu},0<~|\ensuremath{\nu}|<~1,$ confined in a two-dimensional well (with characteristic frequency ${\ensuremath{\omega}}_{0})$ and subjected to an external magnetic field (with cyclotron frequency ${\ensuremath{\omega}}_{c}).$ We apply a variational principle combined with a regularization procedure which consists of fitting a cutoff parameter to existing exact analytical results in the noninteracting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system $|\ensuremath{\nu}|,N,{\ensuremath{\omega}}_{0}{,r}_{0}{,a}_{B}$ and ${\ensuremath{\omega}}_{c},$ where ${r}_{0}$ represents a characteristic unit length and ${a}_{B}$ the Bohr radius. Validity of the result is critically assessed by a comparison with exact, approximate, and numerical results from the literature.

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