Energy projection and modified Laughlin states

TL;DR

This paper introduces an energy projection method to efficiently compute trial wave functions in quantum Hall systems, enabling the study of larger systems and modifications of Laughlin states with improved variational properties.

Contribution

The paper presents a novel energy projection technique that approximates lowest Landau level projection, allowing for larger system studies and testing of modified Laughlin states.

Findings

Energy projection improves variational energy of trial wave functions.

Modified Laughlin states show higher overlap with exact states.

Enhanced entanglement spectrum properties for modified states.

Abstract

We develop a method to efficiently calculate trial wave functions for quantum Hall systems which involve projection onto the lowest Landau level. The method essentially replaces lowest Landau level projection by projection onto the $M$ lowest eigenstates of a suitably chosen hamiltonian acting within the lowest Landau level. The resulting "energy projection" is a controlled approximation to the exact lowest Landau level projection which improves with increasing $M$. It allows us to study projected trial wave functions for system sizes close to the maximal sizes that can be reached by exact diagonalization and can be straightforwardly applied in any geometry. As a first application and test case, we study a class of trial wave functions first proposed by Girvin and Jach, which are modifications of the Laughlin states involving a single real parameter. While these modified Laughlin states probably represent the same universality class exemplified by the Laughlin wave functions, we show by extensive numerical work for systems on the sphere and torus that they provide a significant improvement of the variational energy, overlap with the exact wave function and properties of the entanglement spectrum.