Real Space Effective Interaction and Phase Transition in the Lowest Landau Level

TL;DR

This study uses the DMRG method to analyze phase transitions between stripe and liquid states in the lowest Landau level, revealing how effective interactions influence state stability and correlations.

Contribution

It demonstrates how reductions in effective repulsive interactions at specific distances drive phase transitions and stabilize different quantum Hall states.

Findings

Transition from stripe to liquid at v=3/8 caused by reduced repulsion at r=3

Incompressible states at v=1/3 and 2/5 stabilized by similar interaction reductions

Distinct stripe correlations in the lowest Landau level due to strong short-range interactions

Abstract

The transition between the stripe state and the liquid state in a high magnetic field is studied by the density-matrix renormalization-group (DMRG) method. Systematic analysis on the ground state of two-dimensional electrons in the lowest Landau level shows that the transition from the stripe state to the liquid state at v=3/8 is caused by a reduction of repulsive interaction around r=3. The same reduction of the interaction also stabilizes the incompressible liquid states at v=1/3 and 2/5, which shows a similarity between the two liquid states at v=3/8 and 1/3. It is also shown that the strong short-range interaction around r=1 in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.