Hall Conductivity as the Topological Invariant in the Phase Space in the Presence of Interactions and a Nonuniform Magnetic Field

Zhang, C. X.; Zubkov, M. A.

doi:10.1134/s0021364019190020

Cited by 23 publications

(29 citation statements)

References 16 publications

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“…(The same refers to its inverseQ.) This expectation is based on the recent consideration of the similar question for the quantum Hall effect of systems with interactions (see [66]). Notice, that radiative corrections to the CSE in QED calculated in [47] contain singularities in the limit of vanishing electron or photon mass.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In the present paper we do not consider interactions between the quasiparticles. It is worth mentioning that in the case of Integer Quantum Hall effect the similar problem has been considered recently (see [66]). It has been shown that the expression for Hall conductivity throughĜ has the same form as for the noninteracting case but withĜ replaced by the complete interacting Green function.…”

Section: Introductionmentioning

confidence: 88%

“…In this approach, Weyl-Wigner phase space formalism is used to calculate Dirac operators and Green's functions. These techniques are widely used in recent research [63][64][65][66][67] dealing with linear response to electromagnetic fields which are shown to be topological invariants, as quantum Hall conductance for example.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that the expression for Hall conductivity throughĜ has the same form as for the noninteracting case but withĜ replaced by the complete interacting Green function. Based on the approach of [66] we expect that the same refers to expression for N of Eq. (2).…”

Section: Introductionmentioning

confidence: 99%

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Chiral separation effect in nonhomogeneous systems

Suleymanov

Zubkov

2020

Phys. Rev. D

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We discuss chiral separation effect in the systems with spatial nonhomogeneity. It may be caused by nonuniform electric potential or by another reasons, which do not, however, break chiral symmetry of an effective low energy theory. Such low energy effective theory describes quasiparticles close to the Fermi surfaces. In the presence of constant external magnetic field the nondissipative axial current appears. It appears that its response to chemical potential and magnetic field (the CSE conductivity) is universal. It is robust to smooth modifications of the system and is expressed through an integral over a surface in momentum space that surrounds all singularities of the Green function. In itself this expression represents an extension of the topological invariant protecting Fermi points to the case of inhomogeneous systems.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chiral separation effect in nonhomogeneous systems

Suleymanov

Zubkov

2020

Phys. Rev. D

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“…It is expected that in the presence of the inhomogeneous background (given by the inhomogeneous magnetic field, inhomogeneous rotation, etc) the corresponding conductivities will be given by the topological invariants in phase space composed of the Wigner transformed Green functions. This expectation is based on the recent extension of the topological representation for the Hall conductivity to the case of inhomogeneous magnetic field [17]. The representation of the non -dissipative conductivities in terms of the Wigner transformed propagators may repeat the corresponding homogeneous constructions with the ordinary product replaced by the Moyal product.…”

Section: Discussionmentioning

confidence: 99%

Feynman rules in terms of the Wigner transformed Green functions

Zhang

Zubkov

2020

Physics Letters B

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In the models defined on the inhomogeneous background the propagators depend on the two space -time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations over momenta, which complicate calculations. We propose to express all amplitudes through the Wigner transformed propagators. This approach allows us to reduce the number of integrations. As a price for this the ordinary products of functions are replaced by the Moyal products. The corresponding rules of the diagram technique are formulated using an example of the model with the fermions interacting via an exchange by scalar bosons. The extension of these rules to the other models is straightforward. This approach may simplify calculations in certain particular cases. The most evident one is the calculation of various non -dissipative currents.

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