arXiv subjects

Igor N. Karnaukhov

Publications and source records attributed to Igor N. Karnaukhov.

At least 19 recordsLinked to original sources

arXiv2026

$η$-pairing in a two-band model of spinless fermions

We study the two-band model of spinless fermions in which itinerant fermions interact with localized fermions through the two-particle hybridization. In 1D version, the model has exact solution using the Bethe ansatz. It has been shown that accounting for two-particle hybridization reduces the repulsive interaction between itinerant fermions. In the case of strong interaction, the effective interaction between itinerant fermions is attractive, and $η$-pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to $p$-superconducting states with $η$-pairing. $η$-pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.

cond-mat.str-el↗

arXiv2026

Electron pairing in model with two overlapping bands

We consider the two-band Hubbard model, where electrons from different bands interact through an on-site one- and two-particle hybridization. The proposed Hamiltonian makes it possible to construct an effective theory and answer the question of the nature of pairing: conduction electrons form pairs due to two-particle hybridization of electrons from different bands, compensating for the direct Hubbard repulsion between conduction electrons. It is shown that an effective attraction between conduction electrons leads to $η$-pairing. The electron-electron pairing mechanism explains the presence of superconductivity at high temperatures experimentally observed in hydrogen-rich materials at high pressure.

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arXiv2025

$η$-pairing in the model with two-particle hybridization of conduction and localized electrons

Within the framework of a model, that takes into account two-particle hybridization of conduction and localized electrons, the effective interaction between conduction electrons is calculated. It is shown that this interaction is attractive when the energy of the localized electron corresponding to the two-particle state lies in the conduction band above the Fermi energy. The magnitude of the attractive interaction is minimal for $η$-paired states of conduction electrons. We generalize the original $η$-pairing construction for the proposed model and show that the superconducting state can indeed be realized.

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arXiv2025

Solution of the Anderson chain with two-particle hybridization of localized and itinerant electrons

A modified Anderson lattice is proposed, whose the Hamiltonian accounts for the two-particle hybridization of localized and itinerant electrons instead of one-particle hybridization which takes into account in the original Anderson model. The 1D version of this model can be solved using the Bethe ansazt. It has been shown that hybridization between itinerant and frozen localized electrons results in an effective on-site interaction between itinerant electrons. The magnitude and sign of this interaction depend on the position of the level relative to the Fermi energy (the energy of this level corresponds to the two-particle state of localized electrons at a site). It is shown that when the energy of an localized electron in the two-particle state lies above the Fermi energy, the effective on-site interaction between itinerant electrons is attractive. A repulsive interaction between itinerant electrons occurs when this energy lies below the Fermi energy. Thus, two-part hybridization between localized and itinerant electrons can lead to effective attraction between itinerant electrons, which is unique in itself and may underlie the nature of high-temperature superconductivity.

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arXiv2025

Topological properties of a chain of interacting electrons

Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a finite chain are calculated. The winding number invariant reflects the topological nature of the electron liquid. The phase diagram includes two topological phases with different winding number invariants, the topologically trivial Mott insulator phase, and three critical phase transition points. Numerical calculations confirm and illustrate the analytical results.

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arXiv2024

Solution of one-dimensional Kondo lattice model, ground state calculation

The ground state of the Kondo chain is calculated taking into account the formation of local singlet states of electrons and moments. Singlets are entangled local states of electrons and moments arranged chaotically and varying in time. Two-particle scattering matrix of electrons forming singlets is calculated using the Bethe Ansatz. It is shown that electrons do not hybridize with local moments, and a lattice with a double cell is not formed. In the Kondo insulator a charge gap is calculated for an arbitrary value of the exchange integral. In the case of strong interaction the gap is determined by the single-particle energy of the singlet, for weak interaction - by correlations (the gap is proportional to the square of the exchange integral).

cond-mat.str-el↗

arXiv2024

Composite Hofstadter bands with Dirac fermion spectrum of fractional quantum Hall states

The fractional quantum Hall effect (FQHE) is studied in the semiclassical limit in the framework of the Hofstadter model with a short-range interaction between fermions. In the mean-field approximation, the repulsion between fermions leads to a periodic potential. Numerical calculations show that in the case of the periodic potential with a period that is a multiple on $\frac{1}ν$ of the magnetic cell ($ν$ is filling of a separated band) composite Hofstadter bands (HBs) are formed. The composite HBs are split into $\frac{1}ν$ subbands, which are separated by the Dirac points. The Chern number of $γ$-full filled composite HBs is equal to the Chern number $C_γ$ of the corresponding HB. The Chern number, equal to $νC_γ$, corresponds to $ν$-filling of $γ$-composite HB. Thus, FQHE is realized by fractional filling of composite HBs.

cond-mat.str-el↗

arXiv2023

Mean field approach plus the Bethe ansatz solution of one dimensional models of Kondo insulator

The Kondo insulator (KI) is studyed in the frameworrk of one dimensional models of Kondo and symmentic Anderson lattices at half filling. The consistent application of the mean field approach and the solution using the Bethe ansatz made it possible to come close to solving the problem of the ground state of KI. It is shown, that in ${Z}_2$-field electrons and local moments form singlets at each lattice site. This field leads to an on-site interaction, on which electrons are scattered. In the Kondo chain the Kondo insulator is similar to the Mott insulator in the Hubbard chain. The advantage of proposed approach is that it is possible to solve the problem for arbitrary exchange interaction constant. In the Anderson lattice, the indirect on-site interaction between band electrons is attractive, which makes it possible to propose a new mechanism for high $T_c$ superconductivity in real compounds.

cond-mat.str-el↗

arXiv2023

The ground state of the Kondo lattice

The Kondo insulator state (KIS) is among the least understood phase state in condensed matter physics. KIS is the state of the electron liquid in the Kondo lattice at half filling, is studied within the mean field approach. We demonstrate, that $Z_2$-field, which is formed by electrons and local moments, leads to the state of the Kondo insulator in a lattice with a double cell. In the ground state, electrons and local moments form singlets; in this case, no spin or charge density waves are realized in a lattice with a double cell. We have shown that a Majorana-type gap spectrum of the quasi-particle excitations is realized in $Z_2$-field.8 pages The gap in the spectrum decreases with increasing external magnetic field; it closes at a critical value at the insulator-metal phase transition point. Thus, the introduction of the $Z_2$ -field allows you to answer the key question what is the ground state of KIS.

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arXiv2022

Gapped electron liquid state in the symmetric Anderson lattice, Kondo insulator state

The Kondo insulator state (KIS) realized in the symmetric Anderson model at half filling is studied in the framework of a mean field approach. It is shown that the state of the Kondo insulator is realized in a lattice with a double cell and a gapped electron liquid behaves like a gapless Majorana spin liquid. The local moments of d-electrons form a static $Z_2$-field in which band electrons move. The gap value in the quasi-particle excitations spectrum decreases with increasing an external magnetic field and closes at its critical value. The behavior of an electron liquid is studied for an arbitrary dimension of the model. The proposed approach leads to the description of KIS without the need to resort to artificial symmetry breaking to alternative understanding of the physical nature of this phase state.

cond-mat.str-el↗

arXiv2022

Mott-Hubbard phase transition, gapped electron liquid in insulator stat

Within the framework of a mean-field approach the Mott-Hubbard phase transition is considered in the Hubbard and Falicov-Kimball models for half-filled occupation. It is shown that a static Z_2-field forms an insulator state on the lattice with a double cell, its strength is determined by the Hubbard interaction. An uniform configuration of the Z_2-field corresponds to a gapless spin liquid state, the configuration, at which the lattice with a double cell is formed, corresponds to a gapped fermion liquid, fermions move in this field. Due to the presence of a static field in an insulator state, a formation of a gapped electron liquid is similar to the gapless Majorana spin liquid in Kitaev's model [1]. A gap in the spectrum is calculated depending on the magnitude of the Hubbard interaction for the chain, square and cubic lattices. The proposed approach allows us to describe the Mott-Hubbard phase transition and the insulator state within the same formalism for an arbitrary dimension for different models.

cond-mat.str-el↗

arXiv2022

Electron liquid state in the spin-1/2 anisotropic Kondo lattice

In the framework of the mean field approach, we provide analytical and numerical solution of the spin-1/2 anisotropic Kondo lattice for arbitrary dimension at half filling. Nontrivial solution for the amplitude of the field opens a gap in the fermion spectrum of an electron liquid in which local moments on the lattice sites are realized. The ground state in the insulator state is determined by a static Z_2 field of local moments, which forms the lattice with a double cell, conduction electrons move in this field. Due to hybridization between electron states a large Fermi surface is formed in the Kondo lattice. A gap in the quasi-particle spectrum is calculated depending on the magnitudes of exchange integrals for the simple lattices with different dimension. The proposed approach is also valid for describing the Kondo lattice with weak anisotropy of the exchange interaction, which makes it possible to study the behavior of the spin-1/2 Kondo lattice with an isotropic exchange interaction.

cond-mat.str-el↗

arXiv2021

Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion

In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin-orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin-orbit Rashba coupling and the Coulomb repulsion. The spin-orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. Topological phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The region of existence of the zero energy Majorana states tends to zero at the point of the Mott phase transition. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model

cond-mat.str-el↗

arXiv2021

Mott-Hubbard phase transition in 2D electron liquid

We study the behavior of fermion liquid defined on hexagonal and triangular lattices with short-range repulsion at half filling. In strong coupling limit the Mott-Hubbard phase state is present, the main peculiarity of insulator state is a doubled cell of the lattices. In the insulator state at half filling fermions with momenta $k$ and $k+π$ are coupled via the effective $λ$-field, the gap in the spectrum of quasi-particle excitations opens and the Mott phase transition is occured at a critical value of the one-site Hubbard repulsion~$U_c$. $U_c=3.904$ and $U_c=5.125$ are calculated values for hexagonal and triangular lattices, respectively. Depending on the magnitude of the short-range repulsion, the gap in the spectrum and the energy of the ground state are calculated. The proposed approach is universal; it is implemented for an arbitrary dimension and symmetry of the lattice for fermions models with short-range repulsion.

cond-mat.str-el↗

arXiv2021

Electron pairing in the Hubbard model as a result of on-site repulsion fluctuations

We focus our quantitative analysis on the stability of the insulator state in the Hubbard model at a half-filling. Taking into account large-scale fluctuations (with a long relaxation time) of the on-site Coulomb repulsion, we consider the possibility of realizing a stabile state which is characterized by pairing for electrons. The pairing mechanism is as follows: due to fluctuations of on-site repulsion of electrons, holes, as excited states, are formed electron pairs. The bare values of on-site Coulomb repulsion and its fluctuations, for which the states with electron pairing are stable, are calculated. The proposed pairing mechanism is to some extent similar to the formation of a localized moment in the Wolf model. The calculations were performed for the chain, as well as square and cubic lattices.

cond-mat.str-el↗

arXiv2021

Fractional quantum Hall effect in the Hofstadter model of interacting fermions

Applying a unified approach, we study integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) in the Hofstadter model with short range interaction between fermions. An effective field, that takes into account the interaction, is determined by both the amplitude and phase. Its amplitude is proportional to the interaction strength, the phase corresponds to the minimum energy. In fact the problem is reduced to the Harper equation with two different scales: the first is a magnetic scale (cell size corresponding to a unit quantum magnetic flux), the second scale (determines the inhomogeneity of the effective field) forms the steady fine structure of the Hofstadter spectrum and leads to the realization of fractional quantum Hall states. In a sample of finite sizes with open boundary conditions, the fine structure of the Hofstadter spectrum also includes the fine structure of the edge chiral modes. The subbands in a fine structure of the Hofstadter band (HB) are separated extremely small quasigaps. The Chern number of a topological HB is conserved during the formation of its fine structure. Edge modes are formed into HB, they connect the nearest-neighbor subbands and determine the fractional conductance for the fractional filling at the Fermi energies corresponding to these quasigaps.

cond-mat.str-el↗

arXiv2021

Electron liquid state in the symmetric Anderson lattice

Using mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $\textbf{k}$ and $\textbf{k}+\overrightarrowπ$, the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s-d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

cond-mat.str-el↗

arXiv2020

Mott transition in two-band fermion model with on-site Coulomb repulsion

We provide analytical and numerical solution of the two band fermion model with on-site Coulomb at half filling. In limiting cases for generate bands and one flat band, the model reduces to the Hubbard and Falicov-Kimball models, respectively. We have shown that the insulator state emerges at half filling due to hybridization of fermions of different bands with momenta k and k$+π$. Such hybridization breaks the conservation of the number of particles in each band, the Mott transition is a consequence of spontaneous symmetry breaking. A gap in the spectrum is calculated depending on the magnitude of on-site Coulomb repulsion and the width of the band for the chain, as well as for square and cubic lattices. The proposed approach allows us to describe the formation of the gap in the fermion spectra in the Hubbard and Falicov-Kimball models within the framework of the same mechanism for an arbitrary dimension of the system.

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