Hole-Hole Contact Interaction in the t-J Model

TL;DR

This paper analytically investigates hole-hole interactions in the t-J model, revealing bound states in certain wave channels and their disappearance at higher ratios, with implications for understanding magnetic and nuclear phenomena.

Contribution

It introduces an analytical variational method to calculate hole-hole contact interactions and solves the Bethe-Salpeter equation to find bound states, aligning with numerical results.

Findings

Bound states in d- and p-waves with energies close to numerical results

Disappearance of bound states at t/J ≥ 2-3

Discussion of short-range vs long-range interactions and pion condensation analogy

Abstract

Using an analytical variational approach we calculate the hole-hole contact interaction on the N\'{e}el background. Solution of the Bethe-Salpeter equation with this interaction gives bound states in $d$- and p-waves with binding energies close to those obtained by numerical methods. At $t/J \ge 2-3$ the bound state disappears. In conclusion we discuss the relation between short range and long range interactions and analogy with the problem of pion condensation in nuclear matter.