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

## TL;DR

This paper derives expressions for charge stiffness in low-dimensional hole-doped quantum antiferromagnets, analyzing charge and spin couplings across doping levels to understand pairing mechanisms and charge dynamics.

## Contribution

It introduces generalized charge stiffness expressions for t-J-like models and compares charge and spin correlations in different doping regimes, revealing their behavior and implications for pairing.

## Key findings

- Charge and spin couplings behave similarly in over-doped regions.
- Charge stiffness decreases with doping, indicating reduced Coulomb repulsion.
- t-J-like models can produce attractive interactions under certain conditions.

## Abstract

Expressions for 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 the itinerant antiferromagnetic systems. A detailed comparison between spin and charge correlations and couplings are presented in both strong and weak coupling limits. The result highlights that the charge and spin couplings show very similar behaviour in the over-doped region in both the dimensions, whereas they show a completely different trend in the lower doping regimes. A qualitative equivalence of 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 reduction in the magnitude of effective Coulomb repulsion between the mobile carriers. This leads to an enhanced possibility of fermionic pairing with increase in doping 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 weakly correlated phase, the t-J-like models themselves are able to produce attractive interaction for pairing.