Hubbard operators

The aim of this work is to demonstrate that the above-mentioned unusual properties of cuprates can be interpreted in the framework of the t-J model of a Cu-O plane which is a common structure element of these crystals. The model was shown to describe correctly the low-energy part of the spectrum of the realistic extended Hubbard model [4], To take proper account of strong electron correlations inherent in moderately doped cuprate perovskites the description in terms of Hubbard operators and Mori s projection operator technique [5] are used. The self-energy equations for hole and spin Green s functions obtained in this approach are self-consistently solved for the ranges of hole concentrations 0 < x < 0.16 and temperatures 2 K< T <1200 K. Lattices with 20x20 sites and larger are used. 

We will assume the mesophase director to be parallel to the direction of the static magnetic field. In the last section, III.E, the no-inertia assumption will be rejected and the diffusion operator (2.6) replaced with the complete Hubbard operator. We shall investigate the spectroscopic effects of molecular inertia in the case of an axially symmetric g-tensor. 

Short-range proton correlations have been introduced in the starting Hamiltonian in Ref. 150 that is, the Hubbard operators describing the energy of the hydrogen bond configuration with two possible protons have entered a new term in the total Hamiltonian of the system studied, namely,... 

In particular, this allows the representation of the operators of occupation of hydrogen bonds through the Hubbard operators... 

Ovehinnikov, SG Valkov, W. Hubbard Operators in the Theory of Strongly Correlated Electrons, Imperial College Press London, 2004. 

The Hubbard relation in the frames of the liquid cage model 257 existence of an inverse operator for the right f is sufficient to obtain... 

Only six other centers have operated similar metal bomb calorimeters, mainly modeled on the Hubbard design, and it is therefore of interest to note that Gross and co-workers have been intrepid enough to use a simple two-compartment glass apparatus separated by a break-seal for fluorine combustion (5 atm F2). Their results were in excellent agreement with those obtained in metal bombs (107). 

Here U is the intra-atomic interaction defined in Chapter 4 and t, the hopping integral, is equal to B/2z, where B is the bandwidth and z is the coordination number. The suffixes i and j refer to the nearest-neighbour sites, and aia is the creation operator for site i. The suffix a refers to the spin direction. Hubbard found that a metal-insulator transition should occur when B/U = 1.15. Hubbard s analysis did not include long-range interactions, and therefore did not predict any discontinuity in the number of current carriers. 

Physics described by the model with so many parameters is very rich and the model is able particularly to treat heavy fermion systems. To study the model many approaches were suggested (see reviews [2-5]). They are successful for particular regions of the parameter space but no one is totally universal. In this paper we apply to PAM the generating functional approach (GFA) developed first by Kadanoff and Baym [6] for conventional systems and generalized for strongly correlated electron systems [7-10]. In particular it has been applied to the Hubbard model with arbitrary U in the X-operators formalism [10]. The approach makes it possible to derive equations for the electron Green s function (GF) in terms of variational derivatives with respect to fluctuating fields. 

It is remarkable that Eq.(17) has exactly the same form as in the Hubbard model, only instead of a bare hopping matrix element 112 now we have the induced hopping element A12. Because equations of motion for iF-operators for PAM and the Hubbard model have the same form (with the only change 112 — A12) the equation of motion for a d-electron GF in PAM has the same form as in the Hubbard model [10]. 

The shared features of quantum cell models are specified orbitals, matrix elements and spin conservation. As emphasized by Hubbard[5] for d-electron metals and by Soos and Klein [11] for organic crystals of 7r-donors or 7r-acceptors, the operators o+, and apa in (1), (3) and (4) can rigorously be identified with exact many-electron states of atoms or molecules. The provisos are to restrict the solid-state basis to four states per site (empty, doubly occupied, spin a and spin / ) and to stop associating the matrix elements with specific integrals. The relaxation of core electrons is formally taken into account. Such generalizations increase the plausibility of the models and account for their successes, without affecting their solution or interpretation. 

The Lanczos method has been widely applied to the dynamics in Hubbard and Heisenberg model Hamiltonians[39]. The spectral intensity for an operator O is given by... 

The purpose of these notes is to show how some strongly correlated electron models like the one-band Hubbard model with infinite electron repulsion on rectangular and triangular lattices can be described in terms of spinless fermions and the operators of cyclic spin permutations. We will consider in detail the... 

Abstract. Calculations of the non-linear wave functions of electrons in single wall carbon nanotubes have been carried out by the quantum field theory method namely the second quantization method. Hubbard model of electron states in carbon nanotubes has been used. Based on Heisenberg equation for second quantization operators and the continual approximation the non-linear equations like non-linear Schroedinger equations have been obtained. Runge-Kutt method of the solution of non-linear equations has been used. Numerical results of the equation solutions have been represented as function graphics and phase portraits. The main conclusions and possible applications of non-linear wave functions have been discussed. 

We acknowledge with thanks the co-operation of M.Brouers and D-J.Shi in the ammonium production studies, J.Hubbard and L.Tilling in the preparation of photosystem particles and N.Vlachopoulos and... 

We may recall that the desirability of ensuring size-extensivity for a closed-shell state was one of the principal motivations behind the formulation of the MBPT for the closed-shells. The linked cluster theorem of Bruckner/25/, Goldstone/26/ and Hubbard/27/, proving that each term in the perturbation series for energy can be represented by a linked (connected) diagram directly reflects the size-extensivity of the theory. Hubbard/27/ and Coester/30/ even pointed out immediately after the inception of MBPT/25,26/, that the size-extensivity is intimately related to a cluster expansion structure of the associated wave-operator that is not just confined only to perturbative theory. The corresponding non-perturbative scheme for the closed-shells was first described by Coester and Kummel/30,31/ in nuclear physics and this was transcribed to quantum chemistry... 

The authors would like to thank J. Irby for electron density measurements, A. Hubbard for electron temperature measurements and the Alcator C-Mod operations groups for expert running of the tokamak. Work supported at MIT by DoE Co-operative Agreement No. DE-FC02-99ER54512. This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. 

P. S. Hubbard, Some Properties of Correlation Functions of Irreducible Tensor Operators, Phys. Rev., 180 (1969), 319-326. 

It is known as the three-band Hubbard Hamiltonian [13-15] and can describe the band structure of the parent compounds [16]. Here d (d) and />+ (p) are Fermionic operators for the bands d and p with orbital energy Ed and Ep, respectively. The energy of hopping for an electron (with spin a =t. ) from site i to site j is r. While Up and Ud are Hubbard terms which are present if the occupation number operators rip or rid) are nonzero, Vpd is the intraband Coulomb repulsion. 

Foundations to the CC methods were laid by Coester and Kuemmel,1 Cizek,2 Hubbard,3 Sinanoglu,4 and Primas,5 while Cizek2 first presented the CC equations in explicit form. Also Hubbard3 called attention to the equivalence of CC methods and infinite-order many-body perturbation theory (MBPT) methods. From this latter viewpoint, the CC method is a device to sum to infinity certain classes of MBPT diagrams or all possible MBPT diagrams when the full set of coupled-cluster equations is solved. The latter possibility would require solving a series of coupled equations involving up to IV-fold excitations for N electrons. Practical applications require the truncation of the cluster operators to low N values. 

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