Chiral separation effect in lattice regularization

Abstract

We consider Chiral Separation Effect (CSE) in the lattice regularized quantum field theory. We discuss two types of regularization -with and without exact chiral symmetry. In the latter case this effect is described by its conventional expression for the massless fermions. This is illustrated by the two particular cases -of Wilson fermions and of the conventional overlap fermions. At the same time in the presence of the exact chiral symmetry the CSE disappears. This is illustrated by the naive lattice fermions, when the contributions of the fermion doublers cancel each other. Another example is the modified version of the overlap regularization proposed recently, where there is the exact chiral symmetry, but as a price for this the fermion doublers become zeros of the Green function. In this case the contribution to the CSE of zeros and poles of the Green function cancel each other.

Elastic Deformations and Wigner–Weyl Formalism in Graphene

“…In the present paper we proceed with the development of Wigner-Weyl formalism for the tight-binding models of solid state physics (or, equivalently, for the lattice regularized quantum field theory). We extend the previous works made in this direction 27,28,29,30,31,32,55,56,54 . The developed technique is applied to the class of the inhomogeneous models that includes, in particular, the tight-binding model of graphene in the presence of both inhomogeneous magnetic field and nontrivial elastic deformations.…”

“…It has been used in the field-theoretic kinetic theory 20,21 , in noncommutative field theories 22,23 . Certain applications of the Wigner-Weyl formalism were proposed to several fields of theoretical physics including cosmology 24,25,26 . The Wigner-Weyl formalism has been widely applied to the study of nondissipative transport phenomena 27,28,29,30,31,32 . Using this formalism it has been shown that the response of nondissipative currents to the external field strength is expressed through the topological invariants that are robust to the smooth deformation of the system.…”

“…In the high energy physics the topological invariants in momentum space were considered, say, in 46,47,48,49,50,43,51,52,53 . The Wigner-Weyl formalism in 27,29,31,32 was developed in the context of lattice field theory. The one-particle fermion Green's function G(p, q) was considered in momentum space M (p, q ∈ M).…”

Hall conductivity as topological invariant in phase space

“…In the works of one of the authors of the present paper the Wigner-Weyl formalism has been applied to the study of the nondissipative transport phenomena [47][48][49][50][51][52]. In particular, it was shown that the response of nondissipative currents to the external field strength is expressed through the topological invariants that are robust to the smooth deformations of the system.…”

Chiral response in lattice models of Weyl materials

“…The only lattice studies we are aware of are related to the investigation of the chiral separation effect in a relativistic Dirac plasma [57][58][59]. However, it is still unknown whether the chiral analog of the BZCS term can be derived in the lattice models and whether it enjoys the same topological robustness as its counterpart in the electric current.…”