The spontaneous breaking of noninvertible symmetries can lead to exotic phenomena such as the coexistence of order and disorder. Here, we explore second-order phase transitions in one-dimensional spin chains between two phases that correspond to distinct patterns of noninvertible symmetry breaking. The critical point shares several features with well-understood examples of deconfined quantum critical points, such as enlarged symmetry and identical exponents for the two order parameters participating in the transition. Interestingly, such deconfined transitions involving noninvertible symmetries allow one to construct a whole family of similar critical points by gauging spin-flip symmetries. By employing gauging and bosonization, we characterize the phase diagram of our model in the vicinity of the critical point. We also explore proximate phases and phase transitions in related models, including a deconfined quantum critical point between invertible order parameters that is enforced by a noninvertible symmetry.

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• Order parameters
• Quantum phase transitions
• Symmetry breaking states
• Symmetry protected topological states
• 1-dimensional spin chains
• Strongly correlated systems
• Luttinger liquid model