Quantum anomalies in topological materials and spin chains

Speaker: Prof. Ewelina Hankiewicz 
Affiliation: Physics Department, Würzburg University, Würzburg, Germany

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Recent theoretical and experimental advances allow for an observation of signatures of quantum anomalies in non-interacting condensed matter systems. Quantum anomalies violates one of the classical symmetries and bridge between condensed matter and high- energy physics.

The possibility of observation of signatures of the parity anomaly (failure of the existence of single Dirac fermion in two spatial dimensions characterized by broken parity symmetry) in Dirac-like materials [1,2] is especially interesting. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital field), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly [2]. Moreover, we showed together with experimentalists a novel transition from -1 to 1 Hall plateau, caused by scattering processes between counter-propagating quantum Hall and QAH edge states and parity anomaly [3].

Further, we turn our attention to the conformal anomaly in one-dimensional spin systems. The conformal anomaly signals itself in a breaking of scale invariance by quantum effects, visible in multi-point functions of the energy-momentum tensor. We relate the variance of the on-site static magnetization that could be observed in neutron scattering experiments to the conformal anomaly in these systems. This paves a path to observe quantum anomalies in strongly interacting spin systems [4].

[1] F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
[2] J. Böttcher, C. Tutschku, L. W. Molenkamp, and E. M. Hankiewicz Phys. Rev. Lett. 123, 226602 (2019); C. Tutschku, F. S. Nogueira, C. Northe, J. van den Brink, and E. M. Hankiewicz Phys. Rev. B 102, 205407 (2020); C. Tutschku, J. Böttcher, R. Meyer, and E. M. Hankiewicz Phys. Rev. Research 2, 033193 (2020).
[3] S. Shamim, P. Shekhar, W. Beugeling, J. Böttcher, A. Budewitz, J.-Benedikt Mayer, L. Lunczer, E. M. Hankiewicz, H. Buhmann, L. W. Molenkamp,Nat. Commun. 13, Article number: 2682 (2022).
[4] C. Northe, C. Zhang, S. Galeski and E.M. Hankiewicz submitted to PRL 2022.