Fractional Quantum Hall Effect States on a Torus show a Liquid Insulator Direct Transition

TL;DR

This paper demonstrates that fractional quantum Hall states on a torus can transition directly from a liquid to a Wigner crystal phase without an intermediate quantum phase transition, challenging traditional phase transition understanding.

Contribution

It reveals that the insulator phase can be described by the same wave function as the liquid phase, showing a direct melting or freezing transition.

Findings

Wigner crystal configurations are stable at certain filling factors.

The phase transition occurs without an intermediate quantum phase.

Behavior of the crystal varies with aspect ratio changes.

Abstract

From the Fractional Quantum Hall Effect States on a torus with filling factor nu = 1/p, p odd, we found that for small values of nu such states describe triangular Wigner crystals which are stable configurations. Therefore, the insulator phase of the two-dimensional electron system can be described with the same wave function that the liquid phase, and the incompressible liquid freezes (or the Wigner crystal melts) without any quantum transition between states, thus the system phase changes by means of a direct transition. We found at least one stable configuration of a Wigner crystal with F = 3 electrons for cell and we investigate the behavior of the crystal when the lengths ratio Ly/Lx changes.