Regensburg 2022 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 44: Poster Session: Statistical Physics and Critical Phenomena
DY 44.19: Poster
Donnerstag, 8. September 2022, 15:00–18:00, P2
Multifractality at the integer quantum Hall 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
The quantum Hall transitions are still one of the bigger mysteries of condensed matter theory. In the past twenty years several conjectures have been made as to what the field theory of the critical fixed point of the integer (class A) quantum Hall transition could be. The multifractal spectrum provides a characteristic fingerprint of the phase transition. Here, recent analytical work predicts a parabolic dependency of the anomalous dimension Δq=q(1−q)/4, where the exponents τq=2(q−1)+Δq describe the system-size scaling of wavefunction moments |Ψ|2q [1]. In great analogy to our previous analysis on the spin (class C) quantum Hall transition [2], we investigate the multifractal spectrum of the class A transition and similarly demonstrate the presence of quartic terms in Δq. Our findings are thus clearly inconsistent with the strict parabolicity predicted for "traditional" conformal field theories. [1] M. R. Zirnbauer, Nucl. Phys. B 941, 458 (2019) [2] M. Puschmann et al., Phys. Rev. B 103, 235167 (2021)