Topology of the momentum space, Wigner transformations, and a chiral anomaly in lattice models

Lattice models that can be used to discretize the quantum field theory with massless fermions have been discussed. These models can also be used to describe Dirac semimetals. It has been shown that the axial current for general lattice models should be redefined in order for the usual expression for...

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Bibliographic Details
Published inJETP letters Vol. 106; no. 3; pp. 172 - 178
Main Authors Zubkov, M. A., Khaidukov, Z. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2017
Springer Nature B.V
Subjects
Atomic
Biological and Medical Physics
Biophysics
Divergence
Electromagnetic fields
Fermions
Field theory
Metalloids
Methods of Theoretical Physics
Molecular
Optical and Plasma Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Quantum field theory
Quantum Information Technology
Quantum theory
Solid State Physics
Spintronics
Stability analysis
Topology
Transformations
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Summary:Lattice models that can be used to discretize the quantum field theory with massless fermions have been discussed. These models can also be used to describe Dirac semimetals. It has been shown that the axial current for general lattice models should be redefined in order for the usual expression for the chiral anomaly to remain valid. In this case, in the presence of a time-independent potential of the external electromagnetic field, the formalism of Wigner transformations allows relating the divergence of the axial current to a topological invariant in the momentum space that is defined for a system in equilibrium and is responsible for the stability of the Fermi point. The evaluated expression is the axial anomaly for general lattice models. This expression has been illustrated for models with Wilson fermions.
ISSN:0021-3640
1090-6487
DOI:10.1134/S0021364017150139