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

Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine geometric phases acquired by electronic wave functions as a result of polaron transport around a closed loop. For this study we apply the Lanczos exact diagonalization method to Holstein-Hubbard, Holstein-$tJ$, and Holstein-$tJ_z$ models in order to reveal various aspects of geometric phases. We demonstrate that transverse spin fluctuations are responsible for the generation of nontrivial geometric phases. From the exchange symmetry of polarons we find that the statistical transmutation of polarons occurs depending on the strength of electron correlations.