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International Journal of Modern Physics B

GREEN FUNCTIONS OF STRONGLY CORRELATED ELECTRONS WITH MAGNETIC COUPLING

Nguyen Van Hieu

Published Jan 30, 1996• 1 citation
Publisher

Abstract

The explicit expressions for the imaginary time normal and anomalous two-point Green functions of the strongly correlated itinerant electron (or hole) system with the quantum antiferromagnetic and ferromagnetic couplings and the strong Coulomb repulsion, as well as those of the real time ones at a finite temperature, are derived in the mean field approximation. In the limit of the infinitely strong on-site Coulomb repulsion, the system becomes that with the single occupation constraint.

DOI
10.1142/s0217979296000143

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The explicit expressions for the imaginary time normal and anomalous two-point Green functions of the strongly correlated itinerant electron (or hole) system with the quantum antiferromagnetic and ferromagnetic couplings and the strong Coulomb repulsion, as well as those of the real time ones at a finite temperature, are derived in the mean field approximation. In the limit of the infinitely strong on-site Coulomb repulsion, the system becomes that with the single occupation constraint.
The equation in the ladder approximation was derived for the two-particle Green function of the itinerant electrons with the Heisenberg ferromagnetic and antiferromagnetic interaction. The general form of its solution was found. The existence of the pole in this solution is related to the condensation of the bound pairs in the corresponding spin state. The condition for the pole determines the critical temperature T c . The effective interaction between the mobile holes due to the mobile hole-localized spin coupling in the two-band Hubbard model was also studied.
This work is mainly devoted to the description of processes that involve the interaction between an atom and a surface, in which a strong Coulomb repulsion on the atomic site (U)(U)(U) limits the charge exchange to one electron (infinite-UUU limit). In this limit, the Anderson Hamiltonian for a many-fold (N)(N)(N) of states localized on the atomic site can be represented in terms of auxiliary bosons and physical operators in the mixed boson-electron space can be defined. In this work the Hamiltonian is solved by defining appropriate Green's functions for physical operators. Then we solved the equations of motion of these Green's functions, up to a second order in the atom-surface coupling, either for the stationary case or for a real time-dependent problem. We show that our approach reproduces the known exact results in the nondegenerate (N=1)(N=1)(N=1) case, and for $N\ensuremath{\succ}1$ gives excellent agreement with exact calculations and approximations valid for large NNN (the 1∕N1∕N1∕N expansion). Finally, the accurate description of dynamical processes is shown by the comparison with the exact results available for a small four-level system. In this case we also compare with results obtained by using the noncrossing approximation and with the usual spinless model calculation.
A strongly correlated electronic system is studied within the framework of the t-J model with the help of diagram technique for the Hub- bard X-operators.The summing of some series of diagrams is suggested, corresponding to the following three types of approximations: the generalized random phase approximation, the mean field approximation, and the low density approximation.In generalized random phase approximation the dynamic magnetic susceptibility of paramagnetic phase is calculated, and boundaries of stability of this phase are found on the plane of Hamiltonian parameters and electron concentration n.It is shown that at some critical concentration nc the system undergoes a crossover from the itinerant magnetism (n < n c ) to the magnetism with localized magnetic moments (n > n c ). Simultaneously, the system transfers from the Fermi-liquid beh a v i o u r t o t h e r e g i m e o f s t r o n g e l e c t r o n c o r r e l a t i o n s w i t h n o n q u a s i p a r t i c l e states.In mean field approximation equations for the order parameters were derived and phase transitions temperatures in a ferromagnetic and antiferromagnetic phases were obtained.In low density approximation a state of the saturated ferromagnetism was investigated and a critical concentration n $ was calculated when the nonsaturated ferromagnetism follows the saturated ferromagnetism.
The Hubbard I decoupling approximation [J. Hubbard, Proc. R. Soc. London Ser. A 276, 238 (1963)] is extended by introducing a k-dependent self-energy which describes a mobile correlation hole of opposite spin propagating along with the electron in its way around the lattice. The theory, despite its simplicity, (1) becomes exact in the strong-coupling limit; and (2) reproduces with great accuracy the ground-state energy, the double occupancy, the on-site correlation functions, and the effective hopping for all the values of the Hubbard Coulomb repulsion U. It also gives reasonable spectral functions leading to (3) a single-particle Green function showing the well-known spectral-weight transfer between the Hubbard bands as soon as the electron density deviates from half-filling, and (4) a momentum distribution as well as magnetic and charge structure factors in qualitative agreement with quantum Monte Carlo simulations, slave-boson calculations, and conserving approximations like fluctuation exchange and parquet. On the other hand, as in most decoupling schemes, liftime effects and the near-Fermi-level additional structure characteristic of strongly correlated electron systems are missing.
In the limit of infinite spatial dimensions, a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction ( U < ∞ ), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different "vacuum states".Some analytical results are given for the Hartree-Fock approximation when the 4pole structure for Green's function is obtained: two poles describe contribution from the Fermi liquid component, which is ferromagnetic and dominant for small electron and hole concentrations ("overdoped case" of high-T c 's), whereas other two describe contribution from the non-Fermi liquid, which is antiferromagnetic and dominant close to half filling ("underdoped case").