Sequential quantum phase transitions in ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains with integer spins $(S&gt;1)$: Quantized Berry phase and valence-bond solids

Sequential quantum phase transitions in $J_{1} − J_{2}$ Heisenberg chains with integer spins $(S > 1)$ : Quantized Berry phase and valence-bond solids

Shota Fubasami, Tomonari Mizoguchi, and Yasuhiro Hatsugai

Phys. Rev. B 100, 014438 – Published 30 July 2019

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 in the Berry phase occur $S$ times for spin- $S$ systems, indicating sequential phase transitions. The sequential phase transitions are associated with the change in 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.