Quantum Supercriticality in the Ising Model and Rydberg Atom Array

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 ᵦ (hₓ-hₓᶜ) ^-, correlation length (hₓ-hₓᶜ) ^-, fidelity susceptibility F (hₓ - hₓᶜ) ^d - 2, and entanglement entropy S ₄ (hₓ - hₓᶜ). Here, and represent critical exponents, d is the dimension of the system, and hₓᶜ 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 (hᵦ-hₓ) plane, |hᵦ| (hₓ - hₓᶜ) ^ + relating to critical exponents and, 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.