Regensburg 2019 – wissenschaftliches Programm
HL 8.2: Vortrag
Montag, 1. April 2019, 15:15–15:30, H33
Is the multifractal spectrum at the spin quantum Hall transition exactly parabolic? — •Daniel Hernangómez-Pérez1, Soumya Bera2, Ilya Gruzberg3, and Ferdinand Evers1 — 1Institute of Theoretical Physics, University of Regensburg, Germany — 2Department of Physics, Indian Institute of Technology Bombay, India — 3Department of Physics, Ohio State University, USA
The integer quantum Hall effect (IQHE) has recently been proposed to have an exactly parabolic multifractality spectrum [1, 2]. Due to strong corrections to scaling, however the corresponding exponents are very difficult to access numerically. A close relative of the IQHE (class A) is the spin quantum Hall effect (SQHE, class C). In contrast to IQHE, for SQHE analytical results for certain anomalous exponents are available . Correspondingly, corrections to scaling are under better control. Thus motivated, we here present a numerical study of multifractality at the SQHE using the corresponding network model. Our results: The multifractal spectrum of SQHE obeys the expected symmetry relation ; the analytically known exponents for the LDoS moments, x2= 1/4, x3= 0, are reproduced with good precision: 0.2504 ± 0.008 and 0.000 ± 0.002. The spectrum exhibits significant deviations from parabolicity, i.e. xq/q(3−q) shows linear term a1= 0.0021 ± 0.0002. We see our results as providing constraints for future analytical theories of the SQHE.  R. Bondesan, et al., Nucl. Phys. B 918, 52 (2017).  M. Zirnbauer, arXiv:1805.12555 (2018).  F. Evers et al., Phys. Rev. B 67, 041303(R) (2003).  A. Gruzberg, et al., Phys. Rev. Lett. 107, 086403 (2011).