  Supercriticality, featured with universal scaling behaviors, emerges as an
intriguing phenomenon proximate to the classical liquid-gas critical point. In
this study, we extend this significant concept to quantum many-body systems
near the quantum critical point (QCP), employing tensor network calculations
and scaling analyses of the Ising model and Rydberg atom array. The
supercritical, fluid-like, quantum states are found to be strongly fluctuating
and highly entangled, as characterized by the universal scalings in
susceptibility $\chi_z \sim (h_x-h_x^c)^{-\gamma}$, correlation length $\xi
\sim (h_x-h_x^c)^{-\nu}$, fidelity susceptibility $\chi_F \sim (h_x -
h_x^c)^{d\nu - 2}$, and entanglement entropy $S_{\rm E} \sim \ln{(h_x -
h_x^c)}$. Here, $\gamma$ and $\nu$ represent critical exponents, $d$ is the
dimension of the system, and $h_x^c$ is the critical transverse field of the
Ising QCP. The universal scaling behaviors are revealed in the regime enclosed
by two quantum supercritical crossover lines in the longitudinal-transverse
field ($h_z$-$h_x$) plane, $|h_z| \propto (h_x - h_x^c)^{\beta + \gamma}$
relating to critical exponents $\beta$ and $\gamma$, where the response
functions, measures of entanglement, and fidelity susceptibility reach their
maxima. We propose that Rydberg atom arrays and quantum Ising magnets provide
available platforms for exploring emergent supercritical phenomena and
identifying the universal scalings. The present work establishes a foundation
for exploring quantum supercriticality in magnetic systems and through quantum
simulations.
