Quantum criticality from spectral collapse in the two-photon Rabi model

Abstract

Spectral collapse in the two-photon quantum Rabi model (tpQRM) has long been regarded as incompatible with quantum criticality due to the absence of a vanishing excitation gap. We show that, in the anisotropic tpQRM, spectral collapse constitutes a genuine continuous quantum phase transition governed by a single soft mode. The excitation gap within the same parity closes as $\epsilon_{sp} \sim |g - g_c|^{z\nu}$ with $z\nu = 1/2$, placing the system in the same universality class as the standard QRM, while the gap between different parities reflects symmetry-induced level splitting rather than a critical excitation. This soft mode defines a unique energy scale that controls both equilibrium and nonequilibrium properties, including macroscopic observables, quantum Fisher information, and Kibble-Zurek dynamics. These results establish spectral collapse as an experimentally accessible realization of quantum criticality in a few-body system and demonstrate that universality is fully determined by the soft-mode structure rather than by microscopic details.