Dresden 2017 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 35: Low-Dimensional Systems: 2D - Theory

TT 35.6: Vortrag

Dienstag, 21. März 2017, 15:15–15:30, HSZ 304

Field Theoretical Aspects of Quantum Hall States — •Christian Tutschku, Jan Böttcher, and Ewelina M. Hankiewicz — Institut für Theoretische Physik und Astronomie, Uni Würzburg, 97074 Würzburg, Germany

In condensed matter physics the family of Quantum-Hall (QH) states is one of the most fascinating examples for macroscopic measurable quantum effects. Moreover, the integer, the fractional, the anomalous and the quantum spin Hall effect are of special interest due to their topological origin [1]. All these effects could be described via 2+1 dimensional gauge theories, including topological Chern-Simons (CS) tensor structures of characteristic level [2]. Even if the bare Lagrangian of a theory does not include a CS term, it could be generated at one loop level via contributions of the vacuum polarization operator [3]. If the bare Lagrangian is invariant under a certain symmetry transformation, the one loop correction may also induce an anomaly, which could be related to nonzero off-diagonal eigenvalues of the conductivity tensor [4]. We analyze the formation of CS terms in quantum field theories, describing the different QH states, and show that these terms characterize their topological invariant, their conductivity tensor and their (fractional) statistics. Moreover, we illustrate that the parity anomaly leads to an anomalous QH current.

[1] D. Tong, arXiv:1606.06687 (2016)

[2] G. V. Dunne, arXiv:hep-th/9902115 (1999)

[3] V. R. Khalilov, Theor. Math. Phys. 125 (2000)

[4] A. N. Redlich, Phys. Rev. D 29, 2366 (1984)