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Bulletin of the American Physical Society

Sequential Topological Phase Transitions of J 1 - J 2 Integer Spin Chain

Shota Fubasami, Yasuhiro Hatsugai

Published Mar 8, 2018• 0 citations
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cond-mat.str-elCross-listedarXiv:2607.21705•Jul 27, 2026•0 citations
On the basis of a Berry-phase analysis, we study the ground state of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chain for S=2,3,4S=2,3,4S=2,3,4. We find that changes in the Berry phase occur SSS times for spin-SSS 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 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ 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.
We show that the higher Berry curvature (HBC) can be used to count the gapless edge modes created by an entanglement cut, and thus defines an integer-valued topological order parameter for quantum spin chains. Given an individual spin-chain Hamiltonian, we construct an extending family by interpolating to a reference product Néel state, and show that the integral of the HBC over this extension is equal to the ordinary Berry phase of half of the chain swept out in response to an \textit{infinitesimal} field. It thus counts the spin of the gapless edge modes exposed by the cut, and a change in its integer value signals a phase transition. We illustrate this with several examples: S=1/2S=1/2S=1/2, S=1S=1S=1, and S=3/2S=3/2S=3/2 spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered J1J_1J1​--J2J_2J2​ chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.