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Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point

We show an $\rm O(4)$ symmetry emerges at a deconfined quantum tricritical point of a valence bond solid and two ferromagnetic phases in an $S = 1/2$ frustrated spin chain by combining analytical analysis and numerical calculations with the time evolution of infinite matrix product states. With this symmetry, the valence-bond solid and the three magnetic order parameters form an $\rm O(4)$ pseudovector in the infrared limit, and can continuously rotate into each other. We numerically determine the location of the quantum tricritical point and study the scaling of the correlation functions of the $\rm O(4)$ vector components and associated conserved currents. The critical behaviors of these correlation functions are all in accord with field theoretical results. The emergent $\rm O(4)$ symmetry at the tricritical point is justified by the integer value of the scaling dimension of the emergent Noether conserved currents. Our findings not only give direct evidence of such a high emergent symmetry at an one-dimensional valence bond solid to magnetic transition but also shed light on exploring emergent symmetries in higher dimensions.