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Pronounced - Log T Divergence in Specific Heat of Nonmetallic CeOBiS$_2$: A Mother Phase of BiS$_2$-Based Superconductor

The low-temperature properties of CeOBiS$_2$ single crystals are studied by electrical resistivity, magnetization, and specific heat measurements. Ce 4f -electrons are found to be in a well-localized state split by crystalline-electric-field (CEF) effects. The CEF ground state is a pure $J_z$ = $\pm$ 1/2 doublet, and excited doublets are located far above. At low temperatures in zero field, we observe pronounced $-\log T$ divergence in the specific heat, revealing the presence of quantum critical fluctuations of 4f magnetic moments near a quantum critical point (QCP). Considering that CeOBiS$_2$ is a nonmetal, this phenomenon cannot be attributed to the competition between Kondo and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions as in numerous f-electron-based strongly correlated metals, indicating an unconventional mechanism. We suggest that CeOBiS$_2$ is the first material found to be located at a QCP among geometrically frustrated nonmetallic magnets.