Dynamic simulations of strongly coupled spin ensembles for inferring nature of electronic correlations from nuclear magnetic resonance

We develop an efficient package for the simulation of nuclear magnetic resonance spin echo experiments to study the effects of strong electronic spin correlations on the dynamics of the nuclear spin ensemble. A mean-field model is used to study correlated electronic phases through their hyperfine interaction with nuclear spins. We explore the dynamics of the interacting nuclear ensemble and discuss the key behaviors of the system. In particular, we classify the types of temporal asymmetry that the interaction induces in the system as well as a pulse-dependent shift in the spectral domain. Using these results, we discuss how careful measurement of the pulse-dependent shift can be used to extract information about the anisotropy of the electronic interaction and how these results represent a novel tool for the examination of exotic NMR signatures in strongly correlated materials. Finally, we review specific aspects of the simulation package developed for our exploration and give explicit examples where package can be used to infer range and anisotropy of electronic correlations. In particular, we discuss its structure, accuracy, and the technical merits of the various approximations used to model the nuclear spin ensemble. PROGRAM SUMMARY Program Title: Spin Echo Sim CPC Library link to program files: (to be added by Technical Editor) Repository link: https: //github. com/charlessnider/SpinEchoSim Code Ocean capsule: (to be added by Technical Editor) Licensing provisions: GPLv3 Programming language: Julia, C++, CUDA Nature of problem: Nuclear magnetic resonance studies of strongly correlated electronic materials can result in unexpected or anomalous echo shapes 1. Such shapes can be explained by a long-range nuclear spin-spin interaction 2, 3. However, standard NMR simulations packages are not designed to simulate such large, interacting spin systems. A simulation package designed around the efficient dynamic simulation of large spin ensembles (n > 100, 000) whose interactions can be represented in the mean field limit therefore represents an unexplored yet potent application of numerics to the study of strongly correlated electrons systems in the context of NMR. Solution method: Our open-source CUDA code provides a highly efficient package for the simulation of NMR experiments in the presence of strongly correlated electrons represented in the mean field limit. With full GPU implementation, the simulation performance is hundreds of times faster than standard CPU or hybrid CPU/GPU techniques. The package can accommodate any single-spin or mean field Hamiltonian. A more accessible and easily-adjustable (but less efficient) Julia version of the simulation is included in the code base, as well as tools for the automatic creation of parameter input files for the CUDA simulation.