Bounded by crossover lines exhibiting universal scaling, the supercritical regime above the critical end point is characterized by strong fluctuations and intriguing phenomena. In this study, we extend this notable concept of supercritical crossover to the quantum critical end point (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, $h\ensuremath{\sim}{(g\ensuremath{-}{g}_{c})}^{\mathrm{\ensuremath{\Delta}}}$, is found, where $g$ ( $h$ ) is the transverse (longitudinal) field, ${g}_{c}$ is the critical field, and $\mathrm{\ensuremath{\Delta}}$ 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 a QCEP and associated supercritical crossovers in both equilibrium and nonequilibrium quantum many-body systems.Bounded by crossover lines exhibiting universal scaling, the supercritical regime above the critical end point is characterized by strong fluctuations and intriguing phenomena. In this study, we extend this notable concept of supercritical crossover to the quantum critical end point (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, $h\ensuremath{\sim}{(g\ensuremath{-}{g}_{c})}^{\mathrm{\ensuremath{\Delta}}}$, is found, where $g$ ($h$) is the transverse (longitudinal) field, ${g}_{c}$ is the critical field, and $\mathrm{\ensuremath{\Delta}}$ 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 a QCEP and associated supercritical crossovers in both equilibrium and nonequilibrium quantum many-body systems.

arXiv:2407.05455Physical review. B./Physical review. BNov 17, 202512 citations

Universality and interfaces at critical end points

Michael Ellis Fisher, Paul J. Upton

At a critical end point a critical phase coexists with a noncritical phase \ensuremath{\alpha} and singularities arise beyond those on the associated critical line. New universal amplitude ratios are defined for the shape of the \ensuremath{\alpha}-phase boundary and for the noncritical surface tensions near end points. A postulated correspondence with wall/surface criticality leads to predictions for general dimension d that are exact at (and near) d=2 and for d\ensuremath{\ge}4 (where mean-field theory applies) and yield experimentally testable estimates for d=3.At a critical end point a critical phase coexists with a noncritical phase \ensuremath{\alpha} and singularities arise beyond those on the associated critical line. New universal amplitude ratios are defined for the shape of the \ensuremath{\alpha}-phase boundary and for the noncritical surface tensions near end points. A postulated correspondence with wall/surface criticality leads to predictions for general dimension d that are exact at (and near) d=2 and for d\ensuremath{\ge}4 (where mean-field theory applies) and yield experimentally testable estimates for d=3.

Physical Review LettersNov 5, 1990101 citations

Scaling-Field Approach to Critical Phenomena

Eberhard K. Riedel, Kathie E. Newman

Springer series in solid-state sciencesJan 1, 19830 citations

Critical phenomena and singularities in two complex variables

Clas Blomberg

PhysicaAug 1, 19731 citation

g

(

h

) is the transverse (longitudinal) field,

{g}_{c}

is the critical field, and $\mathrm{\ensuremath{\Delta}}$ 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 a QCEP and associated supercritical crossovers in both equilibrium and nonequilibrium quantum many-body systems.