Study of effective coupling between charge degrees of freedom in low dimensional hole-doped quantum antiferromagnets

Expressions for the generalized charge stiffness constant at zero temperature are derived corresponding to low-dimensional hole-doped quantum antiferromagnets, describable by the t-J-like models, with a view to understanding fermionic pairing possibilities and charge couplings in itinerant antiferromagnetic systems. A detailed comparison between spin and charge correlations and couplings are presented for the strong and weak coupling limits in one (1D) and two (2D) dimensions. The result highlights that the charge and spin couplings show very similar behaviour in the over-doped region in both dimensions, whereas they show a completely different trend in the lower doping regimes. A qualitative equivalence of the generalized charge stiffness constant with the effective Drude weight and Coulomb interaction is established based on the comparison with other theoretical and experimental results. The fall in charge stiffness with increase in doping then implies a reduction in magnitude of the effective Coulomb repulsion between the mobile carriers. This leads to an enhanced possibility of fermionic pairing with an increase in doping concentration, in the possible presence of some other attraction-producing mechanism from a source outside the t-J-like models. Moreover, under certain conditions in the optimal doping region, the t-J-like models themselves are able to produce an attractive interaction for pairing.