Fractionally Quantized Berry Phases Of Magnetization Plateaux In Spin-1/2 Heisenberg Multimer Chains

We study the fractionally quantized Z(N) Berry phase, gamma(N) = 0, 2 pi/N , 4 pi/N, ... , 2(N-1)pi/N, to characterize local N-mer spin structures at magnetization plateaux in spin-1/2 Heisenberg multimer (N-mer) models, i.e., highly frustrated N-leg ladder models, which are generalizations of an orthogonal dimer chain and have exact ground states in the strong multimer coupling region. We demonstrate that all N types of Berry phases, which characterize magnetization-plateau phases, appear in a magnetic phase diagram when N = 2 and 4. We show that magnetization plateau with magnetization < m > and D-fold degenerated states has gamma(N) = pi(< m > - 1)D, except for the Haldane phase with gamma(N) = 0. In addition, we find that a complementary Z(N) Berry phase becomes non-zero in the S = N/2 Haldane phase for N = 2 and 4. Because the exact quantization of the Z(N) Berry phases is protected by the translational (or rotational) symmetry along the rung direction, the Z(N) Berry phase has the potential to be applied for a wide class of magnetization plateaux in coupled multimer systems.