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

## TL;DR

This paper investigates the ground states of higher-spin ($S=2,3,4$) $J_1$-$J_2$ Heisenberg chains using Berry-phase analysis, revealing sequential quantum phase transitions linked to valence-bond configurations.

## Contribution

It demonstrates the occurrence of multiple Berry phase changes in higher-spin chains and connects these to valence-bond-solid states through numerical analysis.

## Key findings

- Sequential Berry phase changes occur $S$ times for spin-$S$ systems.
- Different phases correspond to distinct valence-bond-solid states.
- Numerical connection to generalized AKLT models confirms phase structure.

## 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.