Effective model for the magnon-mediated attraction in the parent cuprates

Using a recently developed method to study magnon-mediated interactions between two holes doped in a cuprate parent compound, we identify four different types of processes which lead to magnon-mediated attraction and show that one of them is dominant. We introduce an effective model for this interaction, allowing us to estimate its coupling strength in the parent cuprates and the critical coupling strength needed to form a bound state. We find that the two values are of the same order of magnitude, indicating that holes in the parent cuprates are close to being bound into pre-formed pairs.