Band effects on the conductivity for a two-band Hubbard model

The band effects on the conductivity of a one-dimensional two-band Hubbard model is studied based on the ground state energy analysis. It is found that the system with filling factor one is a metal at zero temperature if the on-site interaction U is smaller than a critical value U_c, and is an insulator if U is larger than U_c. The value of metal-insulator transition point U_c is obtained. This result is different from that of 1D single-band Hubbard model where the quantum phase transition point U_c=0. Therefore, the orbital degree of freedom plays an essential role in the states of matter.     

Kinematic spin-fluctuation mechanism of high-temperature superconductivity

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ? W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T _c is calculated for various values of U and V.     

Hartree-Fock theory of spiral magnetic order in the 2-d Hubbard model

The magnetic order in the 2-d Hubbard model is investigated within Hartree-Fock theory. For the class of states with uniform particle density and spiral arrangement of spins the phase diagram is obtained by minimizing the free energy. At zero temperature and large Hubbard interactionU there is a continuous transition from the antiferromagnetic solution at half filling over a spiral state of increasing wavelength along the diagonal of the lattice to the ferromagnetic state at doping _c 2t/U. At finite temperatureT, the antiferromagnetic state remains stable for doping smaller than _AF 2T/U. For intermediate values ofU and finite doping there exists also a phase with a spiral wave vector of the form Q=(Q, ).     

Quantum-gas model estimate for wide range of superconducting critical temperatures

A quantum mechanical model requiring only strong quantum interaction for a charged particle gas estimates the superconducting transition temperature for wide-ranging states of matter. A general equation is derived which estimates the critical temperatureT _c the energy gap, and the coherence length for the classical metallic superconductors, heavy-electron superconductors, the perovskites, metallic hydrogen, and neutron stars. Estimates forT _c , the coherence length, and the energy gap which are model independent for coupling mechanisms agree well with accepted values for these materials. Estimates are made for threedimensional quasi-two and quasi-one-dimensional states.     

Theory of superconductivity in strongly correlated materials: Application to cuprate superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high T _c proportional to the Fermi energy. T _c dependence on lattice constants (or pressure) and an oxygen isotope shift of T _c are explained. The text was submitted by the author in English.     

Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff

In this paper we discuss the Eliashberg equations for the case of an electron-phonon coupling with an energy cutoff. This cutoff is imposed either for the energy difference by means of a strip function, or for both energies, with a Cooper-like expression. The strip function cutoff requires explicit calculation of not only the frequency renormalization functionZ but also the energy renormalizationX. The physical origin of such cutoffs might lie in the very strong electron-electron interaction which seems typical for highT _c superconductivity. If such cutoffs are admitted, the hypothesis thatT _c is caused at least in part by a strong electron-phonon interaction can be reconsidered. We find that the combination of strong coupling and low-energy cutoff could produce highT _c with only small isotope effect and with little damping or pulling of the phonon modes. Correlation with other physical properties, such as specific heat, is reexamined in view to estimate the coupling constant . Some objections to the model using strong electron phonon interaction are removed and better agreement with observed properties is obtained     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

Fermi-liquid quasi-particles and -superconductivity in the two-dimensional Hubbard model

A frequency- and momentum-renormalization-group acceleration together with an analytical approach is used to obtain the retarded Green's function in the self-consistent and conserving fluctuation-exchange (FLEX) approximation for the two-dimensional Hubbard model in the normal state and in the superconducting state. The analytical expressions for this approach are given. For band-fillings near half filling the self-energy in the normal state exhibits Fermi-liquid behaviour for, low temperatures and frequencies near the chemical potential, if the momentum is chosen near the Fermi-surface. However due to the presence of large many body effects the observed Fermi-liquid region near the chemical potential and near the Fermi-surface is very small. Results for the single particle density of states, the occupation number and the spectral function are presented. The superconducting state with symmetry is obtained for U = 2 to U = 6 and a (U, n)-phase diagram for the transition temperature T_c is presented. A maximum T_c/t of 0.0275 is obtained for U = 6 near half filling.     

Correlation mediated superconductivity in a “HighT c ” model

We present a simple model to account for the High-T _c perovskite superconductors. The superconducting mechanism is purely electronic and comes from local Hubbard correlations. The model comprises a Hubbard model for the Copper sites with a single particle Oxygen band between the two Copper Hubbard bands. The electrons move only between nearest neighbour atoms which are of different types. Using two very different approximation schemes, one related to Slave-Boson mean field theory and the other based on an exact local Fermion transformation, we show the possibility of Copper-Oxygen or a mixture of Copper-Oxygen and Oxygen-Oxygen pairing. We believe that the most promising situation for superconductivity is with the Oxygen band over half-filled and closer in energy to the lower Hubbard band.     

Quantum Entanglement in Ground State of Extended Hubbard Model

Metal-insulator and CDW-SDW transitions are studied in the one-dimensional Extended Hubbard Model at half-filling by analysing the behaviour of local entanglement in fermionic systems. 1D traditional Hubbard model exhibits metal-insulator transition at critical point U_c = 0, where local entanglement reaches its maximum value. Moreover, a transition between charge- and spin-density- wave (CDW-SDW) occurs in 1D Extended Hubbard Model tUV with long-range interaction at straight line U = 2 V. The analysis of our obtained results shows that CDW-SDW transition has curious properties whose can be used in quantum information processing.

     

Thermodynamics of a 4‐site Hubbard model by analytical diagonalization

By use of the conservation laws a four‐site Hubbard model coupled to a particle bath within an external magnetic field in z‐direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many‐particle states differing in electron number and spin if the electron density is away from half‐filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high‐temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Mott-Hubbard transition in a magnetic field

We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal-insulator transition. E.g., we find an explicit result for the critical value U_c, at which the metal-insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal-insulator transition, occurring in the model with B = 0, is continuously connected to the metal-insulator transition in the subspace of single spin flips.     

Strong coupling Hubbard model and superconductivity

We have shown that systems open to fermion number fluctuations and described by the Hubbard model can be superconducting. This superconductivity must be accompanied by a special type of magnetic order. A unitary transformation is explicitly constructed by which the large interaction term of the Hubbard model is exactly diagonalized. Order parameters of the system related to Green functions of fermions are explicitly evaluated in the strong coupling limit. This model applied to copper-oxygen chains provides a theoretical explanation of highT _c superconductivity in compounds of the type YBa₂Cu₃O_7–x .Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Enhancements of the superconducting transition temperature within the two-band model

The two-band model as introduced by Suhl, Matthias and Walker [Phys. Rev. Lett. 3, 552 (1959)] accounts for multiple energy bands in the vicinity of the Fermi energy which could contribute to electron pairing in superconducting systems. Here, extensions of this model are investigated wherein the effects of coupled superconducting order parameters with different symmetries and the presence of strong electron-lattice coupling on the superconducting transition temperature T_c are studied . Substantial enhancements of T_c are obtained from both effects.Received: 2 July 2003, Published online: 2 April 2004PACS: 74.20.-z Theories and models of superconducting state     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.