Science: Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins

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Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

 

Gonzalo A. Álvarez (1), Dieter Suter (2), Robin Kaiser (3)

(1) Department of Chemical Physics, Weizmann Institute of Science, 76100, Rehovot, Israel.
(2) Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany.
(3) Institut Non-Linéaire de Nice, CNRS, Université de Nice Sophia Antipolis, 06560, Valbonne, France.

Science 349, 846 (2015)

DOI: 10.1126/science.1261160

 

scaling_localization-delocalization_transition
Time evolution of the cluster size of correlated spins K for different quench strengths (1-p) and finite-time scaling procedure. (A) Cluster-size K as a function of the time t after the quench. The unperturbed quenched evolution (black squares) shows a cluster-size K that grows as ∼t^(4.3) at long times (dashed line is a guide to the eye). The solid symbols show the points used for a finite-time scaling analysis, while the empty symbols do not belong to the long time regime (t < 0.3 ms). For the largest perturbation strengths p to the quench, localization effects are clearly visible by the saturation of the cluster size. (B and C) In these two panels, we present the finite-time scaling procedure. In (B), the rescaled and squared correlation length l^2= K^(2/3) as a function of the evolution time 1=t^(k_2) is plotted. In (C), the curves of (B) are rescaled horizontally by the scaling factor ξ(p) to obtain a universal scaling law.

 

localization-delocalization_transition
Scaling factor and critical exponents. Normalized scaling factor ξ(p) as a function of p (blue triangles). The red solid line is a fit to the blue triangles with a expression ξ(p) proportional to|p − p_c|^nu, the critical exponent is then nu= 0,42. The two insets show the distribution of coherence orders of the density matrix as a function of the evolution time t for two perturbation strengths, which correspond to a delocalized and localized regime, respectively. The corresponding scaling factors are indicated by the arrows.

via Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

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