Spin tunneling, Berry phases, and doped antiferromagnets

Interference effects between Berry-phase factors in spin-tunneling systems have been discussed by several groups in the context of quantum magnets. I point out that similar effects appear in the semiclassical analysis of the two-dimensional doped antiferromagnet. As a consequence, the sign of the dispersion of a spin polaron in the t-J model depends on the spin size s in ${\mathit{e}}^{\mathit{i}2\mathrm{\pi }\mathit{s}}$. Thus we arrive at a semiclassical interpretation of the ground-state momentum for the single hole. It agrees with numerical diagonalizations of the t-J model for s=1/2, and predicts a difference between integer- and half-odd-integer-spin cases.