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Universal Edge Transport in Interacting Hall Systems

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Abstract

We study the edge transport properties of 2d interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin–charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof.

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Authors and Affiliations

  1. Institute for Mathematics, University of Zürich, Winterthurerstrasse 190, Zurich, 8057, Switzerland

    Giovanni Antinucci

  2. Department of Mathematics “F. Enriquez”, University of Milano, Via C. Saldini 50, 20133, Milan, Italy

    Vieri Mastropietro

  3. Department of Mathematics, University of Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Marcello Porta

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  1. Giovanni Antinucci
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  2. Vieri Mastropietro
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  3. Marcello Porta
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Correspondence to Marcello Porta.

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Communicated by M. Salmhofer

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Antinucci, G., Mastropietro, V. & Porta, M. Universal Edge Transport in Interacting Hall Systems. Commun. Math. Phys. 362, 295–359 (2018). https://doi.org/10.1007/s00220-018-3192-y

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