SKM 2021 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 9: Poster Session: Correlated Electrons

TT 9.16: Poster

Dienstag, 28. September 2021, 13:30–16:00, P

Multifractality at the spin quantum Hall (class C) transition — •Martin Puschmann¹, Daniel Hernangómez-Pérez², Bruno Lang³, Soumya Bera⁴, and Ferdinand Evers¹ — ¹Institute of Theoretical Physics, University of Regensburg, D-93053 Regensburg, Germany — ²Department of Molecular Chemistry and Material Science, Weizmann Institute of Science, Rehovot 7610001, Israel — ³IMACM and Institute of Applied Computer Science, Bergische Universität Wuppertal, D-42119 Wuppertal, Germany — ⁴Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India

Recent analytical work on the integer quantum Hall transition (class A) predicts a parabolic dependency of the exponents τ_q, that describe the system-size scaling of wavefunction moments |ψ|^2q. [1] The prediction has raised attention, since it contradicts numerical observations [2]. The arguments of [1] rely on conformal invariance and therefore are believed to carry over also to class C. Since in class C corrections to scaling are under control, it provides an excellent laboratory for testing the salient concepts numerically. Thus motivated, we investigate τ_q in class C and eliminate subleading powers guided by finite-size corrections of distribution functions. Thereby, we demonstrate unambiguously the presence of quartic terms in τ_q [3], inconsistent with the predicted parabolic shape but in agreement with [4].
[1] M. R. Zirnbauer, Nucl. Phys. B 941, 458 (2019)
[2] e.g. K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304 (2009)
[3] M. Puschmann et al., Phys. Rev. B 103, 235167 (2021)
[4] J. Karcher et al., arXiv:2107.06414