Quantum aging and dynamical universality in the long-range O(N->?) model

Year: 2021

Authors: Halimeh Jad C.; Maghrebi Mohammad F.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy; Heidelberg Univ, Kirchhoff Inst Phys, Neuenheimer Feld 227, D-69120 Heidelberg, Germany; Heidelberg Univ, Inst Theoret Phys, Philosophenweg 16, D-69120 Heidelberg, Germany; Michigan State Univ, Dept Phys & Astron, E Lansing, MI 48824 USA.

Abstract: 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.

Journal/Review: PHYSICAL REVIEW E

Volume: 103 (5)      Pages from: 052142-1  to: 052142-15

KeyWords: MANY-BODY LOCALIZATION; TIME CRITICAL-BEHAVIOR; RENORMALIZATION-GROUP; GAUGE-INVARIANCE; RELAXATION
DOI: 10.1103/PhysRevE.103.052142

Citations: 9
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