Exact quantization of magnetization plateaux in quantum spin chains

We study the fractionally quantized $Z_N$ Berry phase, $γ_N=0, {2π\over N}, {4π\over N},\ldots, {2(N-1)π\over N}$ , 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 $\langle m\rangle$ and $D$ -fold degenerated states has $γ_N=π(\langle m\rangle-1) D$ , except for the Haldane phase with $γ_N=0$ . 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.We study the fractionally quantized $Z_N$ Berry phase, $γ_N=0, {2π\over N}, {4π\over N},\ldots, {2(N-1)π\over N}$, 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 $\langle m\rangle$ and $D$-fold degenerated states has $γ_N=π(\langle m\rangle-1) D$, except for the Haldane phase with $γ_N=0$. 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.

arXiv:1808.10138Journal of the Physical Society of JapanNov 16, 20188 citations

We study the fractionally quantized

Z_N

Berry phase,

γ_N=0, {2π\over N}, {4π\over N},\ldots, {2(N-1)π\over 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

\langle m\rangle

and

D

-fold degenerated states has

γ_N=π(\langle m\rangle-1) D

, except for the Haldane phase with

γ_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.