Haldane's Fractional Statistics and the Lowest Landau Level on a Torus

TL;DR

This paper investigates the structure of the lowest Landau level on a torus, revealing differences from Haldane's fractional statistics formula, with implications for numerical studies of fractional quantum Hall states.

Contribution

It provides a new calculation of the Hilbert space dimension for the lowest Landau level on a torus, challenging previous formulas by Haldane.

Findings

The Hilbert space dimension differs from Haldane's formula.

Results can be tested through numerical simulations.

Implications for understanding fractional quantum Hall states.

Abstract

The Lowest Landau Level on a torus is studied. The dimension of the many-body Hilbert space is obtained and is found to be different from the formula given by Haldane. Our result can be tested in numerical investigations of the low-energy spectrum of fractional quantum Hall states on a torus.