# Regensburg 2019 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 8: Transport and theory of electronic structure

### 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-Pérez^{1}, Soumya Bera^{2}, Ilya Gruzberg^{3}, and Ferdinand Evers^{1} — ^{1}Institute of Theoretical Physics, University of Regensburg, Germany — ^{2}Department of Physics, Indian Institute of Technology Bombay, India — ^{3}Department 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 [3]. 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 [4]; the analytically known exponents for the LDoS moments, *x*_{2}= 1/4, *x*_{3}= 0, are reproduced with good precision: 0.2504 ± 0.008 and 0.000 ± 0.002. The spectrum exhibits significant deviations from parabolicity, i.e. *x*_{q}/*q*(3−*q*) shows linear term *a*_{1}= 0.0021 ± 0.0002. We see our results as providing constraints for future analytical theories of the SQHE.
[1] R. Bondesan, et al., Nucl. Phys. B **918**, 52 (2017).
[2] M. Zirnbauer, arXiv:1805.12555 (2018).
[3] F. Evers et al., Phys. Rev. B **67**, 041303(R) (2003).
[4] A. Gruzberg, et al., Phys. Rev. Lett. **107**, 086403 (2011).