Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the t-J model. Solving the U = ∞ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction J are then included in a heuristical manner. Formally like in J-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. The obvious importance of antiferromagnetic (AF) correlations for the physics of cuprate superconductors found an impressing confirmation through ARUPS-experiments performed by Aebi et al. [1]. There, in a Fermi surface (FS) mapping of Bi2Sr2CaCu2O8(001) shadows of the FS were observed. The interpretation as an effect of short range antiferromagnetic correlations led to an intensive discussion of so called shadow features, which have been predicted by Kampf and Schrieffer [2] in a semi-phenomenological theory for the Hubbard model. In the paper we present an approximate evaluation of the self energy for the t-J model HtJ consisting of two parts: The hopping term Ht = − t∗
A consequence of strong antiferromagnetic correlations in models of high-Tc cuprates is the appearance in photoemission (PES) calculations of considerable more weight above the Fermi momentum
pF than expected for non-interacting electrons. This effect, first discussed by Kampf and Schrieffer (Phys. Rev. {\bf B 41}, 6399 (1990)) under the name of ``shadow bands'', is here analyzed in the two dimensional Hubbard and t-J models using Monte Carlo and exact diagonalization techniques. It is concluded that for underdoped compounds weight above
pF could be observable in experimental PES data, while in the overdoped regime it will be likely hidden in the experimental background. In the intermediate region the signal is weak. Our results are thus compatible with recent experimental data by Aebi et al. (Phys. Rev. Lett. {\bf 72}, 2757 (1994)) for Bi2212 at optimal doping. However, to definitely prove the existence of this effect in the cuprates, experiments in the underdoped regime are necessary.
Self-energy corrections due to to fermion-magnon interaction are studied in the antiferromagnetic state of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}$ Hubbard model within the noncrossing approximation in the full
U range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,{t}^{\ensuremath{'}},{t}^{\ensuremath{''}}$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states, etc. A finite-
U induced classical dispersion term, absent in the $t\ensuremath{-}J$ model, is found to play an important role in suppressing the quasiparticle weight for states near
k=(0,0), as seen in cuprates. For intermediate
U, the renormalized antiferromagnetic (AF) band gap is found to be nearly half of the classical value, and the weak-coupling limit is quite nontrivial due to strongly suppressed magnon amplitude. For finite ${t}^{\ensuremath{'}}$, the renormalized AF band gap is shown to vanish at a critical interaction strength
Uc, yielding a spin fluctuation driven first-order AF insulator--paramagnetic metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with angle-resolved photoemission spectroscopy data for
Sr2CuO2Cl2.
Away from half filling and above its Neel temperature, the three-dimensional Hubbard model is a paramagnetic metal with antiferromagnetic spin fluctuations, where controlled momentum-resolved results have been lacking. Using connected-determinant diagrammatic Monte Carlo, we compute the momentum-resolved self-energy for n = 0.4-0.95, T/t = 0.05-0.33 and U/t = 4-8, and the full-zone spin susceptibility at twelve of these points, focusing on U/t = 4. At U/t = 4 and toward half filling the spin fluctuations become strong: for n = 0.7-0.9 at T/t = 0.14 they enhance the susceptibility peak up to sevenfold and raise the momentum-dependent part of the scattering rate to four to five times its second-order value. They are driven by an effective spin interaction screened to about 2U/3 and nearly uniform over the zone. Yet the peak height is set by the slightly smaller value of this interaction at the peak wave vector, and near magnetic order this small difference changes the height by a large factor. Two-particle self-consistent theory reproduces the peak because its sum rule fixes its single constant interaction near this value, but for n = 0.7-0.9 at T/t = 0.14 its self-energy overestimates the local scattering rate and underestimates the momentum-dependent part. Though strong, the fluctuations are short ranged, with a correlation length of at most about two lattice spacings, and for n = 0.7-0.9 and T/t >= 0.14 the scattering rate near the Fermi surface varies by at most about 1% at fixed band energy, without hot spots. At U/t = 4 dynamical mean-field theory (DMFT) reproduces the local scattering rate and quasiparticle weight within a few percent, and the nonlocal part it misses is approximately a function of the band energy. Strong spin fluctuations thus coexist with nearly isotropic quasiparticles, and the results provide a benchmark for extensions of DMFT and for spin-fluctuation theories.
Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-
Tc superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.
The theoretical investigation of spectral functions and pseudogap in systems with strongly correlated electrons is discussed, with the emphasis on the single-band t-J model as relevant for superconducting cuprates. The evidence for the pseudogap features from numerical studies of the model is presented. One of the promising methods to study spectral functions is the method of equations of motion. The latter can deal systematically with the local constraints and projected fermion operators inherent for strongly correlated electrons. In the evaluation of the self energy the decoupling of spin and single-particle fluctuations is performed. In an undoped antiferromagnet the method reproduces the selfconsistent Born approximation (SCBA). For finite doping the approximation evolves into a paramagnon contribution which retains large incoherent contribution in the hole part. On the other hand, the contribution of longer-range spin fluctuations is essential for the emergence of the pseudogap. The latter shows up at low doping in the effective truncation of the large Fermi surface, reduced electron density of states and at the same time reduced quasiparticle density of states at the Fermi level.