Quantum aging and dynamical universality in the long-range O(N → ∞) model

Quantum quenches to or near criticality give rise to the phenomenon of aging, manifested by glassylike dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has rejuvenated interest in this phenomenon. Motivated by the ubiquitous long-range interactions in emerging experimental platforms, it is vital to study quantum aging in such settings. In this paper, we investigate the dynamical universality and aging in the d-dimensional O(N) model with the long-range coupling 1/x(d+sigma) and in the mean-field limit N ->infinity that allows an exact treatment. An immediate consequence of long-range coupling is the emergence of nonlinear light cones. We focus on the correlation and response functions, and identify a rich scaling behavior depending on how the corresponding space-time positions are located relative to each other, via a local light cone, and to the time of the quench via a global quench light cone. We determine the initial-slip exponent that governs the short-time dependence of two-point functions. We highlight the qualitative features of aging due to the long-range coupling, in particular in the region outside the light cones. As an important consequence of long-range coupling, the correlation function decays as 1/x(d+sigma) outside the quench light cone while increasing polynomially with the total time after quench. This is while, for short-time differences, the two-time response function equilibrates at all distances even outside this light cone. Our analytic findings are in excellent agreement with exact numerics, and provide a useful benchmark for modern experimental platforms with long-range interactions.

Automated summary

This paper investigates aging and dynamic universality in the d-dimensional O(N) model with long-range coupling and in the mean-field limit N -> infinity. The study reveals the emergence of nonlinear light cones as an immediate consequence of long-range coupling, and identifies rich scaling behavior in correlation and response functions. A notable finding is the decay of correlation function outside the quench light cone while increasing polynomially with total time after quench, with equilibration of two-time response function at all distances for short-time differences even outside the light cone. The analytical findings are in excellent agreement with exact numerics, serving as a useful benchmark for modern experimental platforms with long-range interactions.