Analytical Theory of Strongly Correlated Wigner Crystals in the Lowest Landau Level

TL;DR

This paper develops an analytical theory for strongly correlated Wigner crystals in the lowest Landau level, accurately predicting their energies and phase transitions by approximating composite fermion interactions.

Contribution

It introduces an approximate effective two-body interaction for composite fermions, enabling analytical calculations of Wigner crystal energies and phase boundaries.

Findings

Analytical energies match Monte Carlo simulations.

Predicts discontinuous phase transitions between crystal phases.

Provides insights into compressibility changes at phase boundaries.

Abstract

In this work, we present an analytical theory of strongly correlated Wigner crystals (WCs) in the lowest Landau level (LLL) by constructing an approximate, but accurate effective two-body interaction for composite fermions (CFs) participating in the WCs. This requires integrating out the degrees of freedom of all surrounding CFs, which we accomplish analytically by approximating their wave functions by delta functions. This method produces energies of various strongly correlated WCs that are in excellent agreement with those obtained from the Monte Carlo simulation of the full CF crystal wave functions. We compute the compressibility of the strongly correlated WCs in the LLL and predict discontinuous changes at the phase boundaries separating different crystal phases.