The energy associated with bosonic and fermionic pairs of topological spin defects in doped antiferromagnetic quantum spin-
1∕2 square lattice is estimated within a resonating valence bond scenario, as described by a $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$-like model Hamiltonian, plus a ${t}_{\ensuremath{\perp}}$, responsible of a three-dimensional screening of the electrostatic repulsion within the bosonic pairs. For parameters appropriate for monolayered high-
Tc superconductors, both fermionic and bosonic pairs show ${x}^{2}\ensuremath{-}{y}^{2}$ symmetry. We find a critical value of doping such that the energy of the bosonic pairs goes below twice the energy of two fermionic pairs at their Fermi level. This finding could be related to the onset of high-
Tc superconductivity.
A field theory for the strong-coupling limit of a one-dimensional copper-oxide model is obtained from a weak-coupling point of view. Complementary aspects of strong correlations and band motion are incorporated in a natural way. Doping induces soliton or antisoliton charge excitations into a state with explicity broken chiral symmetry. The solitons or antisolitons have divergent superconductive pairing-correlation functions and various properties reminiscent of doped holes or electrons in high-temperature superconductors.
We define a suitable quantity
Zc that measures the pairing strength of two electrons added to the ground-state wave function by means of the anomalous part of the one-particle Green's function.
Zc discriminates between systems described by one-electron states, like ordinary metals and band insulators, for which
Zc=0, and systems where the single particle picture does not hold, like superconductors and resonating valence bond insulators, for which ${Z}_{c}\ensuremath{\ne}0$. By using a quantum Monte Carlo projection technique for the Hubbard model at
U∕t=4, a finite
Zc, with
d-wave symmetry, is found at half filling and in the lightly doped regime, thus emphasizing a qualitatively new feature coming from electronic correlation.