Exact results for a quantum Hall state with broken rotational symmetry

The most robust fractional quantum Hall state in a strongly correlated two-dimensional system of electrons occurs at one-third filling factor of the lowest Landau level. This state is characterized as an isotropic quantum liquid phase of electrons and is well-described by Laughlin's wave function. The possibility of anisotropic liquid phases of electrons at various filling factors has also been considered via many-body trial wave functions that do not possess rotational symmetry. Several studies employing different approaches and computational methods have been carried out. The inherent many-body nature of a wave function with broken rotational symmetry makes it very cumbersome for analytic calculations. In this work we succeeded to calculate exactly the total energy per particle and all other relevant quantities that correspond to a quantum system of two electrons at one-third filling factor described by a wave function with broken rotational symmetry. The results obtained serve as benchmarks to gauge the accuracy of various numerical methods and simulation techniques used to study the properties of strongly correlated electronic systems of this nature.