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We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory.
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Anomalies in gauge theories ,
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Superstring theory: volume 2, loop amplitudes, anomalies and phenomenology ,
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Electromagnetic Response of Weyl Semimetals ,
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Field Theories of Condensed Matter Physics ,
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Structuring the set of imcompressible quantum Hall fluids ,
J. Frohlich, T. Kerler, U. M. Studer and E. Thiran, · 1995
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Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures ,
S. Das Sarma and A. Pinczuk, · 1996
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Anomalies in quantum field theory ,
R. A. Bertlmann, · 1996
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W(1+infinity) minimal models and the hierarchy of the quantum Hall effect ,
A. Cappelli, C. A. Trugenberger and G. R. Zemba, · 1996
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Conformal Field Theory ,
P. Di Francesco, P. Mathieu and D. Senechal, · 1997
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Direct observation of a fractional charge ,
R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin and D. Mahalu, · 1997
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Topological insulators avoid the parity anomaly ,
M. Mulligan and F. J. Burnell, · 2013
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Axion topological field theory of topological superconductors ,
X.-L. Qi, E. Witten and S.-C. Zhang, · 2013
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A time-reversal invariant topological phase at the surface of a 3D topological insulator ,
P. Bonderson, C. Nayak and X.-L. Qi, · 2013
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Dirac materials ,
T. Wehling, A. Black-Schaffer and A. Balatsky, · 2014
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Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field ,
A. G. Abanov and A. Gromov, · 2014
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Anomalous hydrodynamics of two-dimensional vortex fluids ,
P. Wiegmann and A. G. Abanov, · 2014
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Hall viscosity of hierarchical quantum Hall states ,
M. Fremling, T. H. Hansson and J. Suorsa, · 2014
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Symmetry enforced non-Abelian topological order at the surface of a topological insulator ,
X. Chen, L. Fidkowski and A. Vishwanath, · 2014
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Majorana Zero Modes and Topological Quantum Computation ,
S. Das Sarma, M. Freedman and C. Nayak, · 2015
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Where the Weyl Things Are ,
A. Vishwanath, · 2015
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Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides ,
H. Weng, C. Fang, Z. Fang, B. A. Bernevig and X. Dai, · 2015
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Generalized Bloch theorem and chiral transport phenomena ,
N. Yamamoto, · 2015
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Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases ,
B. Bradlyn and N. Read, · 2015
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Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect ,
A. Gromov, G. Y. Cho, Y. You, A. G. Abanov and E. Fradkin, · 2015
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Topological phases: classification of topological insulators and superconductors of non-interacting fermions, and beyond ,
A. W. W. Ludwig, · 2015
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Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" ,
F. D. M. Haldane, · 2015
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Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators ,
M. A. Metlitski, C. L. Kane and M. P. A. Fisher, · 2015
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Homotopy-Theoretic Approach to SPT Phases in Action: Z 16 Z_{16} Classification of Three-DimensionalSuperconductors ,
A. Kitaev, · 2015
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Fermionic symmetry protected topological phases and cobordisms ,
A. Kapustin, R. Thorngren, A. Turzillo and Z. Wang, · 2015
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Three lectures on topological phases of matter ,
E. Witten, · 2016
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Notes on anomaly induced transport ,
K. Landsteiner, · 2016
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Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels ,
A. G. Grushin, J. W. F. Venderbos, A. Vishwanath and R. Ilan, · 2016
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Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals ,
D. I. Pikulin, A. Chen and M. Franz, · 2016
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Chiral magnetic effect in ZrTe 5 ,
Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosić, A. Fedorov, R. Zhong, J. Schneeloch, G. Gu and T. Valla, · 2016
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Emergent Conformal Symmetry and Geometric Transport Properties of Quantum Hall States on Singular Surfaces ,
T. Can, Y. H. Chiu, M. Laskin and P. Wiegmann, · 2016
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Multipole Expansion in the Quantum Hall Effect ,
A. Cappelli and E. Randellini, · 2016
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Introduction to Quantum Mechanics, second edition ,
D. J. Griffiths, · 2016
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Fermion path integrals and topological phases ,
E. Witten, · 2016
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Gapped boundary phases of topological insulators via weak coupling ,
N. Seiberg and E. Witten, · 2016
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Topology, geometry and quantum interference in condensed matter physics ,
A. G. Abanov, · 2017
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Observed quantization of anyonic heat flow ,
M. Banerjee, M. Heiblum, A. Rosenblatt, Y. Oreg, D. E. Feldman, A. Stern and V. Umansky, · 2017
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Chiral response in lattice models of Weyl materials ,
E. V. Gorbar, V. A. Miransky, I. A. Shovkovy and P. O. Sukhachov, · 2017
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Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons ,
E. V. Gorbar, V. A. Miransky, I. A. Shovkovy and P. O. Sukhachov, · 2017
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Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material ,
F. Reis, G. Li, L. Dudy, M. Bauernfeind, S. Glass, W. Hanke, R. Thomale, J. Schäfer and R. Claessen, · 2017
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Topological superconductors: a review ,
M. Sato and Y. Ando, · 2017
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Bulk-boundary correspondence in the quantum Hall effect ,
A. Cappelli and L. Maffi, · 2018
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Topological Quantum Matter: A Field Theoretical Perspective ,
T. K. Kvorning, · 2018
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Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor ,
T. Kvorning, T. H. Hansson, A. Quelle and C. M. Smith, · 2018
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Landau levels, Bardeen polynomials, and Fermi arcs in Weyl semimetals: Lattice-based approach to the chiral anomaly ,
J. Behrends, S. Roy, M. H. Kolodrubetz, J. H. Bardarson and A. G. Grushin, · 2019
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Choreographed entanglement dances: Topological states of quantum matter ,
X.-G. Wen, · 2019
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A new SU(2) anomaly ,
J. Wang, X.-G. Wen and E. Witten, · 2019
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On the Cobordism Classification of Symmetry Protected Topological Phases ,
K. Yonekura, · 2019
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Torsional Landau levels and geometric anomalies in condensed matter Weyl systems ,
S. Laurila and J. Nissinen, · 2020
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Thermal Nieh-Yan anomaly in Weyl superfluids ,
J. Nissinen and G. E. Volovik, · 2020
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Geometric induction in chiral superconductors ,
Q.-D. Jiang, T. H. Hansson and F. Wilczek, · 2020
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Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory ,
A. Ferraz, K. Gupta, G. Semenoff and P. e. Sodano, · 2020
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Gamma matrices, Majorana fermions, and discrete symmetries in Minkowski and Euclidean signature ,
M. Stone, · 2020
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Thermal transport, geometry, and anomalies ,
M. N. Chernodub, Y. Ferreiros, A. G. Grushin, K. Landsteiner and M. A. H. Vozmediano, · 2021
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Electromagnetic response of topological superconductors ,
M. Stalhammar, M. Stone, M. Sato and T. H. Hansson, · 2021
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Axial-anomaly-induced fermion fractionization and effective gauge-theory actions in odd-dimensional space-times ,
A. J. Niemi and G. W. Semenoff, · 2077
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