spin-$1/2$ model, Eq. \[eq:generalham\].

\
\[tc\]\[tc\][$(J-J_c)/r$]{} \[bc\]\[bc\][$\varphi/\pi$]{}\
\
\[bc\]\[bc\][$|\mathcal{C}|$]{}\

The Bargmann invariants are shown for spin-$1$ chains of lengths $N=5$ (left-hand column) and $N=7$ (right-hand column), and allow for direct comparison and contrast with the spin-$1/2$ case of Fig. \[fig:spinonehalf\]. The circuit is composed of $\mathcal{N} = 100$ vertices. Again, the uppermost row shows the trajectory traced out in the complex plane by the Bargmann invariant as the spin coupling strength is varied from $J_c - 2r$ to $J_c + 2r$. The second row from the top shows the corresponding Bargmann phase; notice that points in the immediate vicinity of the critical point have been disregarded as the phase of a complex number becomes increasingly prone to error as the origin of the complex plane is approached. The next row pictures the overall ‘extent’ of the phase, with the individual pieces of the graph having been joined up end-to-end, as described in section \[section:Results\]. Finally, the magnitude of the Bargmann invariant is shown, and is clearly seen to vanish in the vicinity of the critical point.

Qualitatively, the results for spin-$1$ chains are very similar to those of spin-$1/2$ chains. In particular, the magnitude of the Bargmann invariant still represents 