Quantitative comparisons between theory and experiment in fractional quantum Hall effect*

Comparisons with exact computer experiments have demonstrated the composite fermion theory to be quantitatively accurate at the level of a few percent, but the discrepancy with actual experiments is much larger because of corrections due to finite quantum well width, Landau level mixing and disorder. We carry out detailed calculations for spin phase transitions [1] including the effect Landau level mixing through a non-perturbative fixed phase diffusion Monte Carlo method [2], and find excellent agreement with experimental results. In particular, we explain a substantial difference between spin phase transitions for states at $\nu=n/(2n+1)$ and $\nu=2-n/(2n+1)$ which are related by an exact particle hole symmetry in the absence of Landau level mixing. We also study [3] the competition between the fractional quantum Hall liquid and the crystal phases in the presence of Landau level mixing and explain the re-entrant transitions between FQHE and insulator in the vicinity of $nu=1/3$ in low density hole type samples.

[1] Y. Zhang et al. PRL 117, 116803 (2016); PRB 95, 195105 (2017).
[2] G. Ortiz, D.M. Cepterley, R.M. Martin, PRL 71, 2777 (1993); V. Melik-Alaverdian et al. PRL 79, 5286 (1997); A. D. Guclu and C. J. Umrigar, PRB 71, 045309 (2005).
[3] J. Zhano et al. unpublished.