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

Jad C. Halimeh and Mohammad F. Maghrebi
Phys. Rev. E 103, 052142 – Published 28 May 2021

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/xd+σ and in the mean-field limit N 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/xd+σ 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.

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  • Received 7 September 2020
  • Accepted 29 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052142

©2021 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jad C. Halimeh1,2,3 and Mohammad F. Maghrebi4

  • 1INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
  • 2Kirchhoff Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
  • 3Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
  • 4Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

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Issue

Vol. 103, Iss. 5 — May 2021

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