Quantum Supercritical Crossover with Dynamical Singularity

Abstract: Supercritical states, characterized by strong fluctuations and intriguing phenomena, emerge above the critical point. In this study, we extend this notable concept of supercriticality from classical to quantum systems near the quantum critical point, by studying the one- and two-dimensional quantum Ising models through tensor network calculations and scaling analyses. We reveal the existence of quantum supercritical (QSC) crossover lines, determined by not only response functions but also quantum information quantities. A supercritical scaling law, $h \sim (g - g_c)^{\Delta}$, is revealed, where $g$ ($h$) is the transverse (longitudinal) field, $g_c$ is the critical field, and $\Delta$ is a critical exponent. Moreover, we uncover the QSC crossover line defines a boundary for the dynamical singularity to appear in quench dynamics, which can be ascribed to the intersection between the Lee-Yang zero line and the real-time axis. In particular, when the Hamiltonian parameter is quenched to the QSC crossover line, a singular cusp with exponent 1/2 emerge in the Loschmidt rate function, signaling a new dynamical universality class different from the linear cusp for $h=0$. Possible platforms, such as quantum simulators and quantum magnets are proposed for studying QSC crossovers in experiments. Our work paves the way for exploring QSC crossovers in and out of equilibrium in quantum many-body systems.