Quantum Hall Transitions and Disorder

<strong>Seminar of the School of Physical Sciences --------------------------------------------------</strong> Title:&nbsp;<strong>Quantum Hall Transitions and Disorder</strong> Speaker:&nbsp;<strong>Ravin Bhatt&nbsp;</strong> (Princeton University, Princeton) Date:&nbsp;<strong>October 13, 2016</strong> <strong>Abstract:</strong>&nbsp;It is well known that disorder plays a key role in determining the stability of quantum Hall states and thus the extent of quantum Hall plateaus. As a consequence, there have been several numerical studies of plateau transitions in the integer quantum Hall regime for non-interacting electrons in two dimensions [e.g. 1-5]. By contrast, studies of interacting electrons with disorder in two dimensions in the fractional quantum Hall regime have received relatively less attention in numerical studies. Because of numerical complexity and the challenges therein, there exists just one investigation, performed over a decade ago [6-7], even for the simplest case – the 1/3 fractional quantum Hall state to insulator transition driven by disorder. After reviewing the status of numerical studies as of last year, I will describe our recent numerical investigation [8] of the effect of disorder on quantum entanglement properties of the Laughlin state at 1/3 filling. We find that a suitably defined entanglement entropy function serves as a good diagnostic of the transition from the fractional topological state to an Anderson insulator, and 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. Extension to disorder-driven transitions from other fractional states will be briefly described. * Research supported by United States Department of Energy Office of Basic Energy Sciences References: 1. B. Huckestein and B. Kramer, Phys. Rev. Lett. 64, 1437 (1990) 2. Y. Huo and R. N. Bhatt, Phys. Rev. Lett. 68, 1375 (1992) 3. D.-H. Lee, Z. Wang and S. Kivelson, Phys. Rev. Lett. 70, 4130 (1993) 4. K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304(R) (2009) 5. Q. Zhu, P. Wu, X. Wan and R. N. Bhatt (2016, in preparation) 6. D. N. Sheng, X. Wan, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Phys. Rev. Lett. 90, 256802 (2003) 7. X. Wan, D. N. Sheng, E. H. Rezayi, K. Yang, R. N. Bhatt and F. D. M. Haldane, Phys. Rev. B 72, 075325 (2005) 8. Z. Liu and R. N. Bhatt, arXiv1607.04762 (2016); and in preparation