Real space effective interaction and phase transition in the lowest Landau level

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 ν ∼ 3/8 is caused by a reduction of repulsive interaction around r ∼ 3ℓ. The same reduction of the interaction also stabilizes the incompressible liquid states at ν = 1/3 and 2/5, which shows a similarity between the two liquid states at ν ∼ 3/8 and 1/3. It is also shown that the strong shortrange interaction around r ∼ ℓ in the lowest Landau level makes qualitatively different stripe correlations compared with that in higher Landau levels.