Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

Details Multifractality at the quantum Hall transition: Beyond the parabolic paradigm Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

2008-04-15

arxiv.org/abs/0804.2334v1

Phys. Rev. Lett. 101, 116803 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.101.116803

We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave function moments $<|\psi|^{2q}>$ at the quantum Hall transition. The result reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

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