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Selected universal experimental properties of high temperaturesuperconducting (HTS) cuprates have been singled out in the last decade. One ofthe pivotal challenges in this field is the designation of a consistentinterpretation framework within which we can describe quantitatively theuniversal features of those systems. Here we analyze in a detailed manner theprincipal experimental data and compare them quantitatively with the approachbased on a single band of strongly correlated electrons supplemented withstrong antiferromagnetic (super)exchange interaction (the so-called $t$-$J$-$U$model). The model rationale is provided by estimating its macroscopicparameters on the basis of the 3-band approach for the Cu-O plane. We use ouroriginal full Gutzwiller-wave-function solution by going beyond therenormalized mean field theory (RMFT) in a systematic manner. Our approachreproduces very well the observed hole doping ($\delta$) dependence of thekinetic-energy gain in the superconducting phase, one of the principalnon-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermivelocity in the nodal direction is practically $\delta$-independent and itsuniversal value agrees very well with that determined experimentally. Also, aweak doping dependence of the Fermi wave-vector leads to an almost constantvalue of the effective mass in a pure superconducting phase which is bothobserved in the experiment and reproduced within our approach. An assessment ofthe currently used models is carried out and the results of the canonical RMFTas a zeroth-order solution are provided for comparison to illustrate thenecessity of introduced higher order contributions.

Universal properties of high temperature superconductors from real space pairing: t-J-U model and its quantitative comparison with experiment