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arXiv:1711.01185 · Physical Review X

Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions

Vincent Lienhard, Sylvain de Léséleuc, Daniel Barredo, Thierry Lahaye, Antoine Browaeys, Michael Schuler, Louis-Paul Henry, Andreas Martin Läuchli

Published Jun 18, 2018• 209 citations
arXivHTMLPDF

Abstract

We explore the dynamics of artificial one-and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian.We observe, in a region in parameter space, the onset of antiferromagnetic (AF) ordering, albeit with only finite-range correlations.We study systematically the influence of the ramp speeds on the correlations and their growth in time.We observe a delay in their buildup associated to the finite speed of propagation of correlations in a system with short-range interactions.We obtain a good agreement between experimental data and numerical simulations, taking into account experimental imperfections measured at the single-particle level.Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their buildup in time.

DOI
10.1103/physrevx.8.021070

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Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.