Quantum Supercritical Crossover with Dynamical Singularity

TL;DR

This paper extends the concept of supercritical crossover to quantum critical endpoints, revealing new crossover lines, scaling laws, and dynamical singularities in quantum many-body systems, with potential experimental observation in Rydberg atom arrays.

Contribution

It introduces quantum supercritical crossover lines near QCEP, characterized by response and quantum information measures, and links them to dynamical singularities and universality classes.

Findings

Existence of quantum supercritical crossover lines near QCEP.

A supercritical scaling law $h \,\sim\, (g - g_c)^{\Delta}$ is established.

Dynamical singularities with a cusp and critical exponent 1/2 are identified.

Abstract

Bounded by crossover lines exhibiting universal scaling, the supercritical regime above the critical endpoint is characterized by strong fluctuations and intriguing phenomena. In this study, we extend this notable concept of supercritical crossover to the quantum critical endpoint (QCEP), by studying the prototypical mixed-field quantum Ising and Potts 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, near the QCEP. A supercritical scaling law, $h \sim (g - g_c)^{\Delta}$, is found, where $g$ ($h$) is the transverse (longitudinal) field, $g_c$ is the critical field, and $\Delta$ is the so-called gap exponent of the QCEP. Moreover, we demonstrate that the QSC crossover line acts as a boundary for the emergence of dynamical singularities in quench dynamics. This singularity manifests as a distinctive cusp with a critical exponent of 1/2, signaling a new dynamical universality class. We also propose utilizing Rydberg atom arrays as an experimental platform to observe these QSC crossovers and dynamical singularities. Our work establishes a theoretical framework for understanding the role of QCEP and associated supercritical crossovers in both equilibrium and non-equilibrium quantum many-body systems.