Geometric (Berry) phases and statistical transmutation in the two-dimensional systems of antiferromagnetically correlated electrons

Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine the geometric phases which arise as a result of polaron transport around closed loops. It is of interest to see differences in the geometric phases between the two different systems of antiferromagnets, the Ising antiferromagnets and the Heisenberg antiferromagnets. For this study we apply the Lanczos exact diagonalization method to the Holstein–Hubbard, Holstein-tJ, and Holstein-tJz models. It is shown from this study that the transverse spin interactions (fluctuations) are responsible for the generation of non-trivial geometric phases for the Heisenberg antiferromagnets, unlike the case of the Ising antiferromagnets.