Bulk topology and criticality can both lead to nontrivial boundary effects. Topological orders are often characterized by their robust edge states, while bulk critical points can have different boundary scalings. The interplay between these two different boundary effects is an intriguing problem. The boundary of the deconfined quantum critical point (DQCP) is the ideal platform for the interplay of the two boundary effects, as the DQCP is also an intrinsically gapless symmetry protected topological (igSPT) state. In this work we discuss the boundary of the DQCP and several related models. We demonstrate that the fluctuation of the bulk order parameters and their various boundary conditions lead to a rich possibility of the edge states, including a “pseudogapped” (or super power-law decay) behavior as opposed to the conventional “pristine” (or power-law) behavior. We also briefly discuss the quantum information aspect of our work.

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• Critical phenomena
• Edge states
• Open quantum systems & decoherence
• Surface & interfacial phenomena
• Symmetry protected topological states
• Conformal field theory