arXiv subjects

M. A. Zubkov

Publications and source records attributed to M. A. Zubkov.

At least 19 recordsLinked to original sources

arXiv2026

Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems

We explicitly distinguish Hall viscosity as defined relative to the strain field vs. relative to an emergent vielbein or metric field and discuss it for graphene-like systems. Aside from the gravitational or vielbein/metric related ``geometric'' Hall viscosity prevailing throughout the literature, a contribution proportional to the Hall conductivity, the ``electronic'' Hall viscosity, due to the emergent strain induced gauge field exists. We unify both contributions within the ``emergent'' Hall viscosity, determine it explicitly for graphene in the semimetal and Semenoff semiconducting phases, and in the latter case compare it to its non-relativistic limit. Under these circumstances two topological invariants enter the emergent Hall viscosity in the presence of translation and rotation symmetries. We employ Green function representations for the electronic Hall viscosity, quantized rather generically, and the geometric Hall viscosity, the latter being valid only under Lorentz (or Galilean) symmetry. We discuss experimental perspectives for extracting the emergent Hall viscosity.

cond-mat.mes-hall↗

arXiv2026

Topological invariant responsible for the integer QHE and non-commutative geometry

We consider a wide class of $2D$ tight - binding models of solid state physics. These models are, in the most general case, non - homogeneous. The topological invariant ${\cal N}_3$ responsible for the quantization of the Hall conductivity, for the specific case of the integer quantum Hall effect in $2D$, is expressed through the Wigner transformation of the two-point electron Matsubara Green function. We express this invariant as a pairing of the element of the $K^{-1}$ group (generated by the Green function) with the specific element of the cyclic cohomology group $HC^3$. According to a set of local index theorems the values of ${\cal N}_3$ can be shown to be integer for a limited class of tight - binding models.

cond-mat.mes-hall↗

arXiv2026

Influence of interactions on the chiral effect in $1D$ Dirac semimetal

We consider the 1D Su-Schrieffer-Heeger (SSH) model. It was recently shown that, for the noninteracting model in its Dirac semimetal phase, the linear response of the axial charge density to an external electric field is proportional to the electrical conductivity in the presence of finite dissipation, with the proportionality factor determined by the coupling constants. This relation may be viewed as a manifestation of the chiral effect, which is a dimensional reduction of the 3D chiral magnetic effect. In the present work, we investigate the same model in the presence of two versions of local Hubbard-type interactions using numerical Quantum Monte Carlo simulations. We find, within the numerical resolution and for the parameters studied, that, even in the regime where sufficiently strong interactions drive the system into a Mott insulating phase, the proportionality between the induced axial charge density and the electrical conductivity remains unchanged. This result indicates that the chiral effect is not renormalized by local Hubbard interactions.

cond-mat.str-el↗

arXiv2026

Chiral Magnetic Conductivity in the Tight-Binding Model of Dirac Semimetals

We consider the typical tight - binding model of Dirac semimetal in the presence of both magnetic and electric fields. The electric conductivity reveals dependence on magnetic field. We calculate this dependence in the limit of strong magnetic field, when the given model is described effectively by the one - dimensional SSH model because the dynamics in the plane orthogonal to magnetic field is reduced to that of the lowest Landau level (LLL). Considering the small temperature limit we take into account dissipation due to scattering on impurities. The corresponding dissipation rate is calculated explicitly. The obtained results confirm that the source of the magnetoconductivity in this system is chiral magnetic effect.

cond-mat.mes-hall↗

arXiv2026

Discrete Wigner-Weyl calculus for the finite lattice

We develop the approach of Felix Buot to construction of Wigner-Weyl calculus for the lattice models. We apply this approach to the tight-binding models with finite number of lattice cells. For simplicity we restrict ourselves to the case of rectangular lattice. We start from the original Buot definition of the symbol of operator. This definition is corrected in order to maintain self-consistency of the algebraic constructions. It appears, however, that the Buot symbol for simple operators does not have a regular limit when the lattice size tends to infinity. Therefore, using a more dense auxiliary lattice we modify the Buot symbol of operator in order to build our new discrete Weyl symbol. The latter obeys several useful identities inherited from the continuum theory. Besides, the limit of infinitely large lattice becomes regular. We formulate Keldysh technique for the lattice models using the proposed Weyl symbols of operators. Within this technique the simple expression for the electric conductivity of a two dimensional non - equilibrium and non - homogeneous system is derived. This expression smoothly approaches the topological one in the limit of thermal equilibrium at small temperature and large system area.

cond-mat.mes-hall↗

arXiv2026

Emergent gravity in superplastic crystals

We discuss emergent gravity in the superplastic crystals. We restrict ourselves by the consideration of fermions coupled to gravity. Gravity itself is either Riemannian (without torsion) or teleparallel (no curvature). We demonstrate that in this case the off - diagonal components of stress - energy tensor, being integrated over the whole volume, are topological invariants. In equilibrium their values are not changed if the system is modified smoothly.

gr-qc↗

arXiv2026

Magnetoconductivity of Dirac semimetals and chiral magnetic effect from Keldysh technique

Negative magnetoresistance in Dirac semimetals is typically considered as a manifestation of chiral magnetic effect (CME). The relation between these two phenomena has the status of a hypothesis and is based on sequence of assumptions. We rely on the Keldysh technique of non-equilibrium theory. It allows us to investigate the accumulation of axial charge -- the process that involves both chiral anomaly and relaxation followed by the energy dissipation. We consider the case of strong magnetic field and calculate directly both axial charge density and electric conductivity taking into account both scattering on impurities and interaction with phonons. We obtain the same dependence of axial charge density on electric and magnetic fields, and the same dependence of electric current on axial charge density as the standard heuristic CME calculation. This confirms (in the limit of strong magnetic fields) the hypothesis that the origin of magnetoconductivity in Dirac semimetals is the CME.

cond-mat.mes-hall↗

arXiv2025

Relation between chiral anomaly and electric transport in $1D$ Dirac semimetal

We investigate the interplay of chiral anomaly and dissipation in one - dimensional Dirac semimetal. For definiteness we consider the Su Schrieffer Heeger (SSH) model, which on the language of lattice field theory represents 1 D Wilson fermions. We employ the non-equilibrium Keldysh Green function formalism, and calculate the chiral imbalance and electric conductivity in the presence of energy dissipation, revealing how these observables are connected to the chiral anomaly. By systematically incorporating dissipation effects into the Keldysh framework, we demonstrate how the anomaly-induced contributions manifest in both axial charge density and electric current.

cond-mat.mes-hall↗

arXiv2025

Chiral anomaly in inhomogeneous systems with nontrivial momentum space topology

We consider the chiral anomaly for systems with a wide class of Hermitian Dirac operators ${Q}$ in 4D Euclidean spacetime. We suppose that $ Q$ is not necessarily linear in derivatives and also that it contains a coordinate inhomogeneity unrelated to that of the external gauge field. We use the covariant Wigner-Weyl calculus (in which the Wigner transformed two point Greens function belongs to the two-index tensor representation of the gauge group) and point splitting regularization to calculate the global expression for the anomaly. The Atiyah-Singer theorem can be applied to relate the anomaly to the topological index of $ Q$. We show that the topological index factorizes (under certain assumptions) into the topological invariant $\frac{1}{8π^2}\int \text{tr}(F\wedge F)$ (composed of the gauge field strength) multiplied by a topological invariant $N_3$ in phase space. The latter is responsible for the topological stability of Fermi points/Fermi surfaces and is related to the conductivity of the chiral separation effect.

hep-th↗

arXiv2025

Topological invariant responsible for the stability of the Fermi surfaces in non-homogeneous systems

The topological invariant responsible for the stability of Fermi point/Fermi surface in homogeneous systems is expressed through the one particle Green function, which depends on momentum. It is given by an integral over the 3D hypersurface in momentum space surrounding the Fermi surface. Notion of Fermi surface may be extended to the non - homogeneous systems using Wigner - Weyl calculus. The Fermi surface becomes coordinate dependent, it may be defined as the position of the singularity in momentum space of the Wigner transformed Green function. Then the topological invariant responsible for the stability of this Fermi surface is given by the same expression as for the homogeneous case, in which the Green function is replaced by its Wigner transformation while the ordinary products are replaced by the Moyal products. We illustrate the proposed construction by the examples of the systems, in which the given topological invariant is nontrivial and may be calculated explicitly.

cond-mat.mes-hall↗

arXiv2025

Non-renormalization of the fractional quantum Hall conductivity by interactions

We investigate the theory of the fractional quantum Hall effect (QHE) proposed a long time ago by Lopez and Fradkin \cite{Fradkin1991chern} to describe the principal Jain series. The magnetic fluxes of the statistical gauge field attached to electrons remain at rest in the reference frame moving together with the electron liquid. In the laboratory reference frame the electric field of the statistical gauge field forms and screens the external electric field. The fractional QHE conductivity appears as a consequence of this screening already on the mean field theory level. We consider a relativistic extension of the model, and propose an alternative description of the fractional QHE based on macroscopic motion of the electron liquid within the Zubarev statistical operator approach. It is this macroscopic motion of electrons which in this pattern gives rise to the fractional QHE. Within this approach we propose the proof to all orders of perturbation theory that the interaction corrections cannot change the above mentioned mean field theory result for the QHE conductivity.

cond-mat.mes-hall↗

arXiv2025

Effect of interactions on the topological expression for the chiral separation effect

In the absence of interactions the conductivity of chiral separation effect (CSE) in the system of massless fermions is given by topological expression. Interactions might change the pattern drastically. However, we prove that the CSE conductivity is still given by the topological invariant composed of the Green functions at zero temperature as long as the chiral symmetry is present, and if the renormalized axial current is considered. This allows to predict its appearance with the standard value of conductivity per Dirac fermion $σ_{CSE} = \frac{1}{2 π^2}$ in quark - gluon matter at $T = 0$ and sufficiently large baryon chemical potential, in the hypothetical phase with restored chiral symmetry and without color superconductivity. This phase may be realized inside the neutron stars. We also argue that the same topological expression for the CSE may be observed in Weyl semimetals, which realize the system of interacting relativistic fermions in solid state systems. In order to estimate the non - perturbative corrections to $σ_{CSE}$ within QCD at finite temperatures we apply method of field correlators developed by Yu.A.Simonov. As expected, above the deconfinement crossover the topological expression is approached within the quark - gluon plasma phase, when the quark chemical potential is sufficiently large. However, we observe that this occurs only when quark chemical potential is much larger than the thermal (Debye) mass. This range of parameters appears to be far out of the region accessible at the modern colliders.

hep-ph↗

arXiv2025

Effective Lagrangian for the macroscopic motion of Weyl fermions in $^3$He-A

We consider macroscopic motion of the normal component of superfluid $^3$He - A in global thermodynamic equilibrium within the context of the Zubarev statistical operator method. We formulate the corresponding effective theory in the language of the functional integral. The effective Lagrangian comprising macroscopic motion of fermionic excitations is calculated explicitly for the emergent relativistic fermions of the superfluid $^3$He - A phase immersed in a non-trivial bosonic background due to a space and time dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh-Yan anomaly. We do not consider the dynamics of the superfluid component itself and thereby its backreaction effects due to normal component macroscopic flow. It is being treated as an external background within which the emergent relativistic fermions of the normal component move. The matrix-valued vierbein formulation comprises an additional two dimensional internal spin space for the two axially charged Weyl fermions living at the Fermi points which may be replaced by one featuring a Dirac fermion doublet with a real valued vierbein, an axial Abelian gauge field and a spin connection gauge field mixing the Dirac and internal spin spaces. We carry out this change of description in detail and determine the constraints on the superfluid background as well as the the normal component motion as determined from the Zubarev statistical operator formalism in global thermodynamic equilibrium. As an application of the developed theory we consider macroscopic rotation around the axis of pure integer mass vortices. The corresponding thermodynamic quantities of the normal component are analyzed. Our formulation incorporates both superfluid background flow and macroscopic motion flow of the normal component and thereby enables an analysis of their interrelation.

cond-mat.mes-hall↗

arXiv2025

Generalized Wigner-Weyl calculus for gauge theory and non-dissipative transport

We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by non-trivial background fields interacting with both fermions and gauge bosons. For this theory, a version of Wigner-Weyl calculus is developed, in which the Wigner transformation of the fermion Green function belongs to a matrix representation of gauge group. We demonstrate the power of the proposed formalism through the representation of responses of vector and axial currents to the gauge field strength through the topological invariants composed of the Wigner transformed two-point Green functions. This way a new family of non-dissipative transport phenomena is introduced. In particular, we discuss the non-Abelian versions of the chiral separation effect and of the quantum Hall effect.

hep-th↗

arXiv2024

Weyl orbits as probe of chiral separation effect in magnetic Weyl semimetals

We consider magnetic Weyl semimetals. First of all we review relation of intrinsic anomalous Hall conductivity, band contribution to intrinsic magnetic moment, and the conductivity of chiral separation effect (CSE) to the topological invariants written in terms of the Wigner transformed Green functions (with effects of interaction and disorder taken into account). Next, we concentrate on the CSE. The corresponding bulk axial current is accompanied by the flow of the states in momentum space along the Fermi arcs. Together with the bulk CSE current this flow forms closed Weyl orbits. Their detection can be considered as experimental discovery of chiral separation effect. Previously it was proposed to detect Weyl orbits through the observation of quantum oscillations \cite{Potter_2014} . We propose the alternative way to detect existence of Weyl orbits through the observation of their contributions to Hall conductance.

cond-mat.mes-hall↗

arXiv2023

Effective lagrangian for the macroscopic motion of fermionic matter

We consider macroscopic motion of quantum field systems. Zubarev statistical operator allows to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of functional integral. The effective lagrangian is calculated explicitly for the fermionic systems interacting with dynamical gauge fields. Possible applications to physics of quark - gluon plasma are discussed.

hep-ph↗

arXiv2023

Gravastar-like black hole solutions in $q$-theory

We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of $q$-theory. In this theory Riemannian gravity, as described by the Einstein - Hilbert action, is coupled to a three - form field that describes the dynamical vacuum. Formally it behaves like a matter field with its own stress - energy tensor, equivalent to a scalar field minimally coupled to gravity. The asymptotically flat solutions obtained to the field equations represent black holes. For a sufficiently large horizon radius the energy density is localized within a thin spherical shell situated just outside of the horizon, analogous to a gravastar. The resulting solutions to the field equations, which admit this class of configurations, satisfy existence conditions that stem from the Black Hole no - hair theorem, thanks to the presence of a region in space in which the energy density is negative.

gr-qc↗

arXiv2023

Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions

Hall conductivity for the intrinsic anomalous quantum Hall effect in homogeneous systems is given by the topological invariant composed of the Green function depending on momentum of quasiparticle. This expression reveals correspondence with the mathematical notion of the degree of mapping. A more involved situation takes place for the quantum Hall effect in the presence of external magnetic field. In this case the mentioned expression remains valid if the Green function is taken in a specific representation, where it becomes the infinite - dimensional matrix \cite{Imai:1990zz} or if it is replaced by its Wigner transformation while ordinary products are replaced by the Moyal products \cite{ZW2019}. Both these expressions, unfortunately, are much more complicated and might be useless for the practical calculations. Here we represent the alternative representation for the Hall conductivity of a uniform system in the presence of constant magnetic field. The Hall conductivity is expressed through the Green function taken in Harper representation, when its nonhomogeneity is attributed to the matrix structure while functional dependence is on one momentum that belongs to magnetic Brillouin zone. Our consideration for the interacting systems is non - perturbative and is based on the Schwinger - Dyson equations truncated in a reasonable way. We demonstrate that in this approximation the expression for the Hall conductivity in Harper representation remains valid, where the interacting Green function is to be used instead of the non - interacting one. We, therefore, propose that the obtained expression may be used for the topological description of fractional quantum Hall effect.

cond-mat.mes-hall↗