Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain-analogies to deconfined quantum critical points

We study a 1D system that shows many analogies to proposed 2D deconfined quantum critical points. Our system is a translationally invariant spin-1/2 chain with on-site Z2×Z2 symmetry and time reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all on-site symmetries are restored while the translation symmetry is broken. The other Z2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition and the characterization of the VBS phase. The transition has a description in terms of either two domain wall species that "fractionalize" the VBS order parameter or in terms of partons that "fractionalize" the FM order parameter. The two descriptions are dual to each other. We also find an exact reformulation of the transition that leads to a simple field theory description that explicitly unifies the two order parameters, which can be interpreted as a new parton approach that encodes the two order parameters in instantons.