  Deconfined quantum criticality describes continuous phase transitions that
are not captured by the Landau-Ginzburg paradigm. Here, we investigate
deconfined quantum critical points in the long-range, anisotropic Heisenberg
chain. With matrix product state simulations, we show that the model undergoes
a continuous phase transition from a valence bond solid to an antiferromagnet.
We extract the critical exponents of the transition and connect them to an
effective field theory obtained from bosonization techniques. We show that
beyond stabilizing the valance bond order, the long-range interactions are
irrelevant and the transition is well described by a double frequency
sine-Gordon model. We propose how to realize and probe deconfined quantum
criticality in our model with trapped-ion quantum simulators.
