27p-ED-1 Berry's Phase and Fractional Quantization of Adiabatic Motion

Robert G. Littlejohn

Toshikaze Kariyado, Yasuhiro Hatsugai

Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming the existence of an adiabatic process that protects the quantization of the Berry phase, a nontrivial Berry phase $\ensuremath{\gamma}\ensuremath{\propto}2\ensuremath{\pi}\ensuremath{\rho}$ ($\ensuremath{\rho}$ is the local filling of particles) for the bulk suggests appearance of edge states with boundaries. We have applied this generic consideration for the Bloch states of a two-dimensional model with massless Dirac fermions where $\ensuremath{\gamma}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ implies the edge states. The entanglement entropy is evaluated for the models and its relation to the bulk-edge correspondence of Dirac fermions is discussed as well.

Ali Mostafazadeh

Hiroshi Kuratsuji, Shinji Iida

Shin Miyahara

Spin-1/2 frustrated Heisenberg model show novel ground states due to the quantum fluctulation. To classify the ground states with toprogical invariant, we introduce fractionally quantized Berry phase. The Berry phase for the Heisenberg model is defined by local spin twists in the spin xy plane. As typical examples, we consider plateau states in frustrated magnets, e.g., a multimer ( N -mer) chains. Fractional quantization of the Berry phase comes from rotational symmetry of the twisted cluster. The Z N Berry phases are obtained from the numerical integration with using the ground states calculated by the Lanczos method. As a result, we obtained fractional quantization of Z 2 and Z 4 Berry phases in dimer ( N =2) and tetramer ( N =4) chains respectively.

Yves Brihaye, Piotr Kosiński