Detecting symmetry fractionalization by magnetic impurities

Experimental detection of quantum spin liquids (QSLs) and the phenomena of symmetry fractionalization therein has been a long-lasting problem. We study the Kondo problem of a magnetic impurity coupled to a gapped Z2 QSL with crystal symmetries. Remarkably, when the spinon excitations in the QSL exhibit certain nontrivial class of crystal symmetry fractionalization, there will be a non-Kramers doublet protected by crystal symmetries even when the impurity is Kondo screened by the QSL. We demonstrate this unconventional Kondo effect by exact solvable model and large-N calculations. This points to a new way to detect symmetry fractionalization in QSL materials.