Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

TL;DR

This study investigates how anisotropic Coulomb interactions affect fractional quantum Hall states, revealing phase transitions from liquid to smectic and crystalline phases, and introduces model wave functions to describe these states.

Contribution

It demonstrates the evolution of fractional quantum Hall states under anisotropic interactions and proposes a family of model wave functions for different phases.

Findings

Weak anisotropy preserves incompressible liquid state

Increased anisotropy leads to Hall-smectic-like phase

Strong anisotropy results in a crystal phase

Abstract

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].