Electron states in the two-band Hubbard model: Paramagnetic phase

The electron energy spectrum of the copper-based oxides is calculated in the two-band Hubbard model. The conditions for the onset of a localized spin state are studied. The effect of doping is also studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 94–104, 1990.     

A diagram method for the two-band Hubbard model

The two-band Hubbard model is considered within the framework of a diagram technique designed to take strong electronic correlations into account.In memory of Professor D.N. ZubarevInstitute of Applied Physics, Academy of Sciences of Moldova. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 270–282, November, 1993.     

Magnetic and superconductive states in the repulsive Hubbard model

It is shown that antiferromagnetic, ferromagnetic, and superconductive states are possible in the repulsive Hubbard model. The role of small denominators of the Green functions and the Van Hove saddle points in the phase transitions is discussed. It is shown that superconductivity is possible if and only if one of the Van Hove saddle points is situated near the Fermi level. The Cooper pairing arises in channels with odd angular momenta. (It is the p-pairing in the first approximation.) The optimal mutual position of the Van Hove saddle point and the Fermi level corresponding to the maximal critical temperature is found. The problem of the coexistence of superconductivity and ferromagnetism is discussed. Bibliography: 25 titles. Dedicated to L. D. Faddeev on the occasion of his 60th birthday Published inZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 264–284. Translated by V. N. Popov.     

Superconductive states in the two-dimensional repulsive Hubbard model

The investigation of the two-dimensional repulsive Hubbard model is continued for the case in which the Fermi level is close to one of the saddle Van Hove points of the quasiparticle energy function. The Bethe-Salpeter equation for the two-particle scattering amplitude and the system of Dyson-Gor'kov equations for normal and anomalous Green functions are considered. The closeness of the Van Hove point to the Fermi level makes the investigation substantially simpler. A new method of evaluating the kernel of the equations, i.e., the oneloop polarization diagram, is suggested. It is shown that a nontrivial Cooper pairing (the superposition of the pairings with odd angular momenta) appears in the model if and only if the Fermi level is close to one of the Van Hove points. The temperature of the superconductive phase transition is maximal for some special mutual location of the Fermi level and the Van Hove point. Two different superconductive solutions (modes) are found which are antisymmetric functions in the momentum representation. These modes coexist in close vicinity of the doping parameter value corresponding to the intersection of the Van Hove point and the Fermi level. The values of the energy gap for these modes are, generally speaking, different (the two different gap values are observed in some experiments). Bibliography: 18 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 147–176. Translated by V. N. Popov.     

Antiferromagnetic and superconducting states in the three-band two-dimensional repulsive Hubbard model

The three-band two-dimensional repulsive Hubbard model in the formalism of the temperature Green function is investigated. The applicability of the weak coupling approach at the values of the dimensionless coupling constant U/t≈10–11 is justified. The normal state, the antiferromagnetic state with Neel magnetic ordering on the “copper” sublattice, and the superconducting state with nontrivial Cooper pairing in channels with odd angular momenta are studied. The possibility of other magnetic states in the model is discussed. Bibliography: 20 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 194–228. Translated by K. Malyshev.     

Collective excitations in the ferro-and antiferromagnetic states of the two-dimensional repulsive Hubbard model

Collective excitations in the antiferromagnetic and ferromagnetic states of the two-dimensional repulsive Hubbard model are investigated both in the phase transition vicinity (Ginsburg-Landau region |T−T_c|≪T_c) and in the low-temperature region T≪T_c using the functional integration method. The spectrum of collective excitation consists of one branch at T>T_c, and another branch (Goldstone branch) arises at T<T_c. The Goldstone branch at T≪T_c in the antiferromagnetic state is calculated including the anisotropic correction term to the linear dispersion law. The value of the nonphonon branch at the zero momentum is equal to the double gap of the fermion energy 2Δ. All the spectrum branches in the ferromagnetic state vanish at zero momentum . Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 229–259. Translated by P. A. Sevastianov.     

Symmetry tower in the Hubbard model

For the example of the Hubbard model, it is shown that a symmetry tower exists in strongly correlated systems. As a consequence, models with strong interelectron interaction are more appropriately regarded as generators of models. Dynamical algebras that form the tower are found. It is conjectured that the solution to the currently most complicated problem of strong interelectron correlation reduces to analysis of the category of the groups that determine the specific symmetry tower.Perm State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 75–83, January, 1992.     

The functional integral in the Hubbard model

In a new functional integral approach proposed for the model, we find the regime with a deformed integration measure in which the standard integral is replaced with the Jackson integral. We indicate the relation to a p-adic functional integral. For the magnetic and electronic subsystems in the effective functional that results from the operator formulation of the Hubbard model, we find the two-parametric quantum derivative resulting in the appearance of the quantum SU_rq (2) group. We establish the relation to the one-parametric quantum derivative and to the standard derivative.     

Electron-phonon superconductivity mechanisms in the Hubbard model

An electron-phonon pairing mechanism in the Hubbard model on a square lattice is considered. The method of two-time Green's functions is used to calculate the critical temperature of the superconducting transition. The limiting caseU is considered, and expressions are obtained for the dependences on the concentration of particles of the temperatures of the superconducting and Peierls transitions and the exponent of the isotopic effect. It is shown that the inclusion of Coulomb correlations leads to a displacement of the Van Hove singularity in the quasiparticle spectrum and to a change in the dependences of the isotopic effect and the temperatures of the superconducting and Peierls transitions on the carrier concentration compared with an ordinary Fermi system.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 463–473, June, 1992.     

Dynamic spin susceptibility in the Hubbard model

The dynamic spin susceptibility in the Hubbard model is calculated on the basis of the new diagram technique developed for systems with strong correlation. In the leading-order approximation, the singlesite interaction is allowed and electron hopping is taken into account using the evolution operator. The second order of perturbation theory is considered and the sum of 1PI two-particle single-site diagrams of the ladder type is calculated. The equations for calculating the static susceptibility and the spin wave spectrum are obtained. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 124–138, October, 1997.     

Exact solution for the thermodynamics of the one-dimensional Hubbard model with infinite repulsion in a magnetic field

We demonstrate that in the limit of infinite repulsion in a magnetic field, the canonical partition function of the one-dimensional Hubbard model in the nearest-neighbor approximation factors into the product of partition functions of holons and spinons, which can be calculated exactly. We thus obtain exact numerical dependences of the free energy, entropy, internal energy, specific heat, chemical potential, and magnetic susceptibility on the hole concentration, temperature, and magnetic field induction.     

Diagram technique for the Hubbard model

Institute of Applied Physics, Moldavian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 428–437, March, 1990.     

Supergroup approach to the Hubbard model

Based on the revealed hidden supergroup structure, we develop a new approach to the Hubbard model. We reveal a relation of even Hubbard operators to the spinor representation of the generators of the rotation group of four-dimensional spaces. We propose a procedure for constructing a matrix representation of translation generators, yielding a curved space on which dynamic superfields are defined. We construct a new deformed nonlinear superalgebra for the regime of spinless Hubbard model fermions in the case of large on-site repulsion and evaluate the effective functional for spinless fermions     

Correlation functions of the one-dimensional Hubbard model

Conclusions We have investigated the critical behavior of the Hubbard model with attraction. To investigate the critical behavior of the model with repulsion, it is sufficient to use a unitary electron-hole transformation [3,8], and then the SCP correlation function will correspond to the spin-wave correlation function (the parameters of the models can be readily recalculated).The quasione-dimensional generalization of the investigated system can be used as a model of a high-temperature superconductor with chemical pairing mechanism [16,25].Leningrad Branch, V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 331–348, March, 1990.