Aspects of Time-Dependent Critical Phenomena

M. P. Kawatra, J. I. Budnick

Michael Ellis Fisher

Karthik Chinni, Pablo M. Poggi, Ivan H. Deutsch

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization, are fragile and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs those that depend on local trajectories.

Kyozi Kawasaki

Dynamical behaviors of magnetic systems near the critical points in the nonhydrodynamical regime are considered. For this purpose we construct a kinetic equation to describe the time evolution of critical fluctuations that corresponds in a sense to the Boltzmann equation of dilute gases. A graphical technique is developed to deduce the self-consistent equation for time-correlation functions of critical fluctuations from this kinetic equation, and the properties of the time-correlation functions of spin fluctuations for the Heisenberg isotropic and planar ferro- and isotropic antiferromagnets are discussed. The results are then applied to the high-frequency sound attenuation in magnetic systems.

G. Toulouse

Fan Yang, Shao-Jian Jiang, Fei Zhou

Quantum phase transitions are usually classified into discrete universality classes that typically only depend on symmetries and spatial dimensionalities. In this Letter, we demonstrate an opportunity to continuously vary the critical exponents or universalities by tuning experimental parameters in a given physical system. Particularly, we show that critical exponents in long-range spin systems simulated in ion traps can be easily tuned with laser detuning. We suggest that such experiments also effectively simulate some aspects of critical phenomena in conventional spin systems but in artificial non-integer spatial dimensions.