Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids

Abstract

On the basis of a Berry-phase analysis, we study the ground state of the $J_1$-$J_2$ Heisenberg chain for $S=2,3,4$. We find that changes of the Berry phase occur $S$ times for spin-$S$ systems, indicating the sequential phase transitions. The sequential phase transitions are associated with the change of valence-bond configurations of the ground states. To demonstrate this numerically, we connect the $J_1$-$J_2$ Heisenberg Hamiltonian with the generalized Affleck-Kennedy-Lieb-Tasaki model, and show that the different phases are connected to the different valence-bond-solid states.

7pages, 7 figures

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Cited by in corpus (7)

• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Higher order topological matter and fractional chiral states
• Plateau transitions of spin pump and bulk-edge correspondence
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Realization of Wess-Zumino-Witten transitions with levels $k=6$ and $k=4$ in a frustrated spin-3 chain
• Topological Phases in Half-Integer Higher Spin $J_1$-$J_2$ Heisenberg Chains