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A. A. Ovchinnikov

Publications and source records attributed to A. A. Ovchinnikov.

At least 19 recordsLinked to original sources
arXiv2024

Bosonization and correlators of the one-dimensional Hubbard model

We present simple derivation of the Luttinger liquid relation for the 1D Hubbard model both for finite $U$ and in the $U=\infty$ limit. We describe the simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and a physical way using the Bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary $U$ through the single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and a physically transparent way.

cond-mat.str-el↗
arXiv2022

Lattice local integrable regularization of the Sine-Gordon model

We study the local lattice integrable regularization of the Sine-Gordon model written down in terms of the lattice Bose-operators. We show that the local spin Hamiltonian obtained from the six-vertex model with alternating inhomogeneities in fact leads to the Sine-Gordon model in the low-energy limit. We show that the Bethe Ansatz results for this model lead to the correct general relations for different critical exponents of the coupling constant.

math-ph↗
arXiv2020

Threshold singularities in the XXZ- spin chain

We calculate the critical exponents of the threshold singularity for the spectral density of the XXZ- spin chain at zero magnetic field for the lower threshold. We show that the corresponding phase shifts are momentum-independent and coinside with the predictions of the effective mobile impurity Hamiltonian approach. We show that for the eigenstates with the high-energy particle with the momentum $k$ which is much larger than the momenta of the particle-hole excitations the formfactor is not described in the framework of the Luttinger model even in the limit $k<<p_F$ but should be evaluated in the framework of the effective mobile impurity Hamiltonian approach.

cond-mat.stat-mech↗
arXiv2019

The interaction energy of the particle-hole pair in the XXZ-spin chain

We calculate directly the interaction energy of the eigenstate with the single particle and the single hole for the XXZ-spin chain. We find the connection of this addition to the energy with the two-particle forward scattering phase shift function. The results can have applications to the calculation of the exponents of the threshold singularities in the correlators of the XXZ-spin chain.

math-ph↗
arXiv2018

Jain hierarchy for the Fractional Quantum Hall Effect

We propose the effective hierarchical partition function which is able to describe both the Jain states and the Jain-type hierarchical states. Using this partition function (effective Lagrangian) we calculate the charge of the quasiparticle excitations. We show that the Jain-type hierarchical states are equivalent to the system of anyons in the external magnetic field.

cond-mat.mes-hall↗
arXiv2016

Threshold singularities in the correlators of the one-dimensional models

We calculate the threshold singularities in one-dimensional models using the universal low-energy formfactors obtained in the framework of the non-linear Luttinger liquid model. We find the reason why the simplified picture of the impurity moving in the Luttinger liquid leads to the correct results. We obtain the prefactors of the singularities including their $k$- dependence at small $k<<p_F$.

math-ph↗
arXiv2015

Baxter Q- operator and functional relations

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from the explicit calculations. We derive the Baxter equation from the well known fusion relations for the transfer matrices. Our method is valid for an arbitrary integrable model corresponding to the quantum group $U_q(\hat{sl}_2)$ for example for the XXZ- spin chain.

math-ph↗
arXiv2013

On the particle excitations in the XXZ- spin chain

We continue to study the excited states for the XXZ- spin chain corresponding to the complex roots of the Bethe Ansatz equations with the imaginary part equal to $π/2$. We propose the particle-hole symmetry which relates the eigenstates build up from the two different pseudovacuum states. We find the XXX- spin chain limit for the eigenstates with the complex roots. We also comment on the low-energy excited states for the XXZ- spin chain.

math-ph↗
arXiv2012

On the asymptotic expansion of the correlators in the XX spin chain

Using the XX- spin chain as an example we show that in general the asymptotic expansion of the correlator at large distances is not given by the sum over the low-lying particle-hole intermediate states. Only the first two terms in the expansion agree with the predictions of the Luttinger liquid theory. The other terms are in general given by the intermediate states with the particles and holes with the quantum numbers far away from the Fermi- points (at the distances of order of the length of the chain). We argue that the whole expansion cannot be described by the Luttinger liquid theory.

math-ph↗
arXiv2011

On the universal relations for the formfactors in 1D quantum liquids

For various one-dimensional quantum liquids in the framework of the Luttinger model (bosonization) we establish the relations between the coefficients before the power-law asymptotics of the correlators (prefactors) and the formfactors of the corresponding local operators. The derivation of these relations in the framework of the bosonization procedure allows to substantiate the prediction for the formfactors corresponding to the low-lying particle-hole excitations. We present an explicit expressions for the particle-hole formfactors for various one-dimensional models. We also obtain the formulas for the summation over the particle-hole states corresponding to the power-law asymptotics of the correlators.

math-ph↗
arXiv2011

On the universal relations for the prefactors in correlation functions of 1D quantum liquids

For various one-dimensional quantum liquids in the framework of the Luttinger model (bosonization) we establish the relations between the coefficients before the power-law asymptotics of the correlators (prefactors) and the formfactors of the corresponding local operators. The derivation of these relations in the framework of the bosonization procedure allows to substantiate the prediction for the formfactors corresponding to the low-lying particle-hole excitations. We also obtain the formulas for the summation over the particle-hole states corresponding to the power-law asymptotics of the correlators.

math-ph↗
arXiv2008

Fisher-Hartwig conjecture and the correlators in the inpenetrable Bose gas

We apply the theorems from the theory of Toeplitz determinants to calculate the asymptotics of various correlators including the exponential ones in the inpenetrable one-dimensional Bose gas system. The known correlators in the free-fermion system are also used to test the generalized Fisher-Hartwig conjecture.

math-ph↗
arXiv2008

The lengths distribution of laminar phases for type-I intermittency in the presence of noise

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [PRE 62 (2000) 6304] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

nlin.CD↗
arXiv2004

Determination of the mass of the LambdaLambda dibaryon by the method of QCD sum rules

The method of QCD sum rules is used to calculate the mass of a hypothetical stable dihyperon H with the quantum numbers of two Lambda hyperons, whose existence was predicted by R.L. Jaffe [Phys. Rev. Lett. 31, 195, 617(E) (1977)] in the framework of the MIT quark-bag model. Within the accuracy of the method of QCD sum rules, which in the present case is 20%, the results obtained here agree with those of Jaffe. However, the method of sum rules does not make it possible to determine whether the mass of the dihyperon H lies above or below the Lambda Lambda threshold (i.e., whether H is stable).

hep-ph↗
arXiv2004

Formfactors and functional form of correlators in the XX spin chain

We present the new expressions for the formfactors of local operators for the XX - quantum spin chain as a Cauchy determinants. Using the known functional form of the correlator at large distances we propose the new expression for the constant for the asymptotics of the correlator as a Cauchy determinant. We calculate the momentum distribution for the general case of the XXZ spin chain and point out that it is completely different from the Luttinger model (the system of fermions). For the XX chain we compare numerically the value of the lowest formfactor and the expectation value of momentum- zero operators which is determined by the functional form of the correlator.

math-ph↗
arXiv2003

Two-dimensional tunnel bifurcations with dissipation

Two-particle tunneling in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. We show that the use of the proposed model is justified by a comparison with realistic potential energy surfaces of porphyrin and experimental dependence of the reaction rate on temperature. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.

cond-mat.soft↗
arXiv2003

Two-dimensional tunnel correlations with dissipation

Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.

cond-mat.mes-hall↗