Finite Size Scaling in Quantum Hallography

Details Finite Size Scaling in Quantum Hallography Finite Size Scaling in Quantum Hallography

2011-12-16

arxiv.org/abs/1112.3698v1

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, 8 figures

Scientific paper

At low temperatures observations of the Hall resistance for Quantum Hall systems at the interface between two Hall plateaux reveal a power-law behaviour, $\exd R_{xy}/\exd B \propto T^{-p}$ (with $p = 0.42 \pm 0.01$); changing at still smaller temperatures, $T < T_s$, to a temperature-independent value. Experiments also show that the transition temperature varies with sample size, $L$, according to $T_s \propto 1/L$. These experiments pose a potential challenge to the holographic AdS/QHE model recently proposed in {\tt arXiv:1008.1917}. This proposal, which was motivated by the natural way AdS/CFT methods capture the emergent duality symmetries exhibited by quantum Hall systems, successfully describes the scaling exponent $p$ by relating it to an infrared dynamical exponent $z$ with $p = 2/z$. For a broad class of models $z$ is robustly predicted to be $z = 5$ in the regime relevant to the experiments (though becoming $z = 1$ further in the ultraviolet). By incorporating finite-size effects into these models we show that they reproduce a transition to a temperature-independent regime, predicting a transition temperature satisfying $T_s \propto 1/L$ even though $z = 5$. The AdS/CFT calculation predicts this is a first-order transition, suggesting new possibilities for testing the picture. Remarkably, in this interpretation the gravity dual of the transition from temperature scaling to temperature-independent resistance is related to the Chandrashekar transition from a star to a black hole with increasing mass.

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