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Physical review. B, Condensed matter

Self-energy approach to thet-Jmodel

Maciej M. Maśka

Published Jul 1, 1993• 9 citations
Publisher

Abstract

An approach to the problem of single-occupancy constraint in the t-J model is presented. In order to project out the states of double occupied sites, the electronic self-energy is introduced in an effective Hamiltonian. The self-energy is derived by applying the self-consistent moment method to the Hubbard model with infinite on-site Coulomb repulsion.

DOI
10.1103/physrevb.48.1160

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The equation for the charge vertex \ensuremath{\gamma} of the t-J model is derived and solved in leading order of a 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on \ensuremath{\gamma} are then calculated, such as the lifetime and the transport lifetime of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on J and are mainly determined by the constraint of having no double occupancies of sites. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9608053•Physical review. B, Condensed matter•Oct 1, 1996•32 citations
An approach to the problem of single-occupancy constraint in the t-J model is presented. In order to project out the states of double occupied sites, the electronic self-energy is introduced in an effective Hamiltonian. The self-energy is derived by applying the self-consistent moment method to the Hubbard model with infinite on-site Coulomb repulsion.
We reconsider the strong-coupling expansion for the Hubbard model recently introduced by Sarker and Pairault et al. By introducing slave particles that act as projection operators onto the empty, singly occupied and doubly occupied atomic states, the perturbation theory around the atomic limit distinguishes between processes that do conserve or do not conserve the total number of doubly occupied sites. This allows for a systematic t/U expansion that does not break down at low temperature (t being the intersite hopping amplitude and U the local Coulomb repulsion). The fermionic field becomes a two-component field, which reflects the presence of the two Hubbard bands. The single-particle propagator is naturally expressed as a function of a 2×2 matrix self-energy. Furthermore, by introducing a time- and space-fluctuating spin-quantization axis in the functional integral, we can expand around a "non-degenerate" ground-state where each singly occupied site has a well defined spin direction (which may fluctuate in time). This formalism is used to derive the effective action of charge carriers in the lower Hubbard band to first order in t/U. We recover the action of the t–J model in the spin-hole coherent-state path integral. We also compare our results with those previously obtained by studying fluctuations around the large-U Hartree–Fock saddle point.
The t - J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the ` t model', or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labelled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite U Hubbard model with infinite-range hopping -t>0 .
Slave bosons are commonly introduced in order to implement an infinite Hubbard U by means of a local constraint. The usual starting point for investigations within this scheme is a mean-field theory in which the constraint is taken to be global. This approximate treatment of the constraint is studied in the context of a two-band Hubbard model, and it is shown that (i) the ground state has a significant number of doubly occupied sites, despite the infinite on-site repulsion in the original model, and (ii) there is an unphysical tendency for pairing. However, it is found that if the local constraint is retained for the insulator at half filling, then mean-field theory gives the correct result that the double occupancy is zero.
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.
The equation for the charge vertex \ensuremath{\gamma} of the t-J model is derived and solved in leading order of a 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on \ensuremath{\gamma} are then calculated, such as the lifetime and the transport lifetime of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on J and are mainly determined by the constraint of having no double occupancies of sites. \textcopyright{} 1996 The American Physical Society.