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Over the past few decades, tremendous efforts have been devoted tounderstanding self-duality at the quantum critical point, which enlarges theglobal symmetry and constrains the dynamics. In this letter, we employlarge-scale density matrix renormalization group simulations to investigate thecritical spin chain with long-range interaction $V(r) \sim 1/r^{\alpha}$.Remarkably, we reveal that the long-range interaction drives the deconfinedcriticality towards a first-order phase transition as $\alpha$ decreases. Morestrikingly, the emergent self-duality leads to an emergent symmetry andmanifests at these first-order critical points. This discovery is reminiscentof self-duality protected multicritical points and provides the example of thecritical line with generalized symmetry. Our work has far-reaching implicationsfor ongoing experimental efforts in Rydberg atom quantum simulators.

Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition