Localization of isolated holes in a Mott insulator and delocalization by pairing

I have calculated the ground-state energy and wave function of a single (pair of) hole(s) moving in a two-dimensional antiferromagnetically correlated background in the self-retracing-path approximation within the t-J model. The confining potential due to the string of overturned spins is treated quasistatically in the strong-coupling limit. I find that (i) an isolated hole is autolocalized at discrete energy levels, broadened presumably into narrow resonances due to failure of the quasistatic approximation, (ii) a pair of holes bind for J/t>0.45 in the dilute limit δ→0, but (iii) higher concentration favors delocalization of holes by pairing. This has observable consequences for the normal-state transport and optical absorption in the high-Tc cuprate superconductors