  The intermediate behavior near a quantum phase transition is crucial for
understanding the quantum criticality of various competing phases and their
separate origins, yet remains unexplored for the multiple Yu-Shiba-Rusinov
(YSR) states. Here, we investigated the detailed spectroscopic change of the
exchange coupling-dependent YSR states near a quantum phase transition. The
initially developed one pair of YSR states, induced by the Fe vacancy in
monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution
showing an evolution into two pairs of YSR peaks yet with dichotomy in their
spectral features. Interestingly, while the lower-energy YSR branch enters the
quantum phase transition region, the higher-lying one remains rigidly away from
the lower-energy counterpart with a constant energy difference. Spectral weight
analysis of the higher-energy branch yields an exponential dependence on the
exchange coupling, which can be well rationalized by taking the two pairs of
YSR states as a result of field splitting by the magnetic anisotropy. Our
results unveil the intermediate region of a quantum phase transition with a
magnetic anisotropy-induced splitting of the YSR resonance, and highlight a
prospect for developing functional electronics based on the flexibly
controllable multiple quantum states.
