Disorder plays a key role in determining the stability of quantum Hall states and thus the extent of quantum Hall plateaus. Thus there have been several numerical studies of plateau transitions in the integer quantum Hall regime for non-interacting electrons in two dimensions. In contrast, studies of interacting electrons in the fractional quantum Hall regime have received relatively less attention because of computational complexity. After reviewing previous studies [1-2], I will describe our recent investigations at addressing this numerically challenging issue. First, I will present results of the effect of disorder on quantum entanglement properties of fractional quantum Hall ground states [3-4], and show that a suitably defined entanglement entropy function serves as a good diagnostic of the transition from the fractional topological state to an Anderson insulator. It provides a numerically more efficient method of locating the transition than previous methods; further, it enables a study of the critical behavior, not obtainable previously. Following that, we will study excited state properties in the presence of disorder, and present numerical evidence concerning the possibility of many-body localization in Landau levels [5].
[1] D. N. Sheng, X. Wan, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Physical Review Letters 90, 256802 (2003)
[2] X. Wan, D. N. Sheng, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Physical Review B 72, 075325 (2005)
[3] Zhao Liu and R. N. Bhatt, Physical Review Letters 117, 206801 (2016)
[4] Zhao Liu and R. N. Bhatt, Physical Review B 96, 115111 (2017)
[5] Scott D. Geraedts and R. N. Bhatt, Physical Review B 95, 054303 (2017)