Abstract
A systematic diagrammatic expansion for Gutzwiller wavefunctions (DE-GWFs) proposed very recently is used for the description of the superconducting (SC) ground state in the two-dimensional square-lattice t–J model with the hopping electron amplitudes t (and ) between nearest (and next-nearest) neighbors. For the example of the SC state analysis we provide a detailed comparison of the methodʼs results with those of other approaches. Namely, (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results and (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed ‘grand-canonical Gutzwiller approximation’ (called either GCGA or SGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a wave only for optimally and overdoped systems, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the k-space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly correlated systems, as it (i) works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to that of the GA (i.e., it provides the results much faster than the VMC approach).
Highlights
The Hubbard and the t–J models of strongly correlated fermions play an eminent role in rationalizing the principal properties of high-temperature superconductors
The difference between the variational Monte Carlo (VMC)-like DE-Gutzwiller wavefunction (GWF) and the full DE-GWF scheme shows that neglecting longer-range gap and hopping components can lead to a decrease of the principal gap component by up to 37% and the corresponding decrease of the condensation energy by 3 ÷ 35%
It can be seen that such a method is able to yield quite accurate results for the condensation energy and the effective gap in the t–J model
Summary
The Hubbard and the t–J models of strongly correlated fermions play an eminent role in rationalizing the principal properties of high-temperature superconductors (for recent reviews see [2, 10, 37, 47, 53]). No single unifying approach, if possible at all, exists in the literature which would unify the Eliashberg-type and the real-space approaches, out of which a Cooper-pair condensate would emerge as a universal state for arbitrary ratio of the band energy ∼W to the Coulomb repulsion U This exclusive character of the approaches is ascribed to the presence of the Mott–Hubbard phase transition that takes place for W U ≈ 1 (appearing for the half-filled band case), which delineates the physics in the strong-correlation limit for a doped-Mott metallic state, for W substantially smaller than U.
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