D ec 1 99 2 Spin Tunneling , Berry phases and Doped Antiferromagnets

Interference effects between Berry phase factors in spin tunneling systems have been discussed in recent Letters by Loss, DiVincenzo and Grinstein (LDG) [1] and von Delft and Henley (vDH) [2]. As physical realizations, LDG proposed tunneling of magnetic clusters, and vDH proposed an anisotropic spin hamiltonian and the Heisenberg antiferromagnet on the Kagomé lattice. In these examples, for certain spin sizes s, the classical ground state degeneracies are not lifted by tunneling processes. This Comment points out that Berry phases in spin tunneling are important in another interesting case: the two dimensional doped antiferromagnet. This model is often used to describe cuprate superconductors. We shall see that the Berry phases of Refs. [1, 2] can explain the ground state momentum of the single hole, as found by finite size numerical simulations of the t-J model [3]. In Ref. [4], the hole in the antiferromagnet has been cast as a spin tunneling problem. First the t-J model was extended to s >