We propose a novel mechanism of impurity screening in $(1+1)d$ quantum critical states described by conformal field theories (CFTs). An impurity can be screened if it has the same quantum numbers as some gapless degrees of freedom of the CFT. The common source of these degrees of freedom is the chiral primary fields of the CFT, but we uncover that topological defect lines of the CFT may also take this role. Theoretical analysis relies on the insight that the impurities can be interpreted as edge modes of certain symmetry-protected topological (SPT) states. By stacking a SPT state with a CFT, one or two interfaces on which the SPT edge modes reside are created. If screening occurs due to topological defect lines, a symmetry-enriched CFT with exotic boundary states is obtained. The boundary conditions that appear in these cases are difficult to achieve using previously known methods. As a concrete example, we consider a spin-1 chain whose bulk is described by the ${\mathrm{SU}(3)}_1$ CFT and edges are coupled to spin-$1/2$ impurities. We demonstrate that both the low-energy eigenstates and the extracted Affleck-Ludwig entropy are in excellent agreement with our theoretical predictions.

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• Quantum criticality
• Topological phase transition
• 1-dimensional systems
• Conformal field theory
• Quantum spin chains