Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains

Abstract

We study the fractionally quantized $Z_N$ Berry phase, ${\gamma }_N=0,\frac{2\pi }{N},\frac{4\pi }{N},\dots ,\frac{2(N-1)\pi }{N}$, 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.

arXiv comment5 pages, 4 figures

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Cited by in corpus (7)

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• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Magnetic phase diagrams of the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain: Emergence of a Haldane phase
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Ferromagnetic Haldane state and dimer multiplet state of quantum ferromagnets
• $Z_2\times Z_2$ symmetry and $Z_4$ Berry phase of bosonic ladder