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.

💡 Research Summary

This paper presents an open‑source, GPU‑accelerated simulation package (“Spin Echo Sim”) designed to model nuclear magnetic resonance (NMR) spin‑echo experiments in materials where electronic spins are strongly correlated. The authors start by noting that conventional NMR simulation tools (e.g., PULSEE, SIMPSON) are limited to weakly interacting or non‑interacting spin systems and cannot handle the large ensembles (>10⁵ spins) required to capture long‑range, electron‑mediated nuclear‑nuclear couplings. To overcome this, they integrate out the electronic degrees of freedom and adopt a mean‑field description of the hyperfine interaction, yielding an effective Hamiltonian in which each nuclear spin experiences a site‑dependent mean field Mᵢ. This field is expressed as Mᵢᵈ = αᵈ ∑ⱼ f(|rᵢ − rⱼ|)⟨Iⱼᵈ⟩, where αᵈ encodes anisotropic electronic susceptibility and f(r, ξ) describes the spatial range of the interaction set by the electronic correlation length ξ.

The simulation propagates the full time‑dependent Hamiltonian under arbitrary pulse sequences, allowing direct calculation of spin‑echo waveforms and their Fourier spectra. By implementing the core propagation kernels in CUDA and providing a higher‑level Julia interface, the package achieves speed‑ups of two to three orders of magnitude over CPU‑only codes while maintaining numerical convergence with respect to time step and system size.

Systematic studies varying αᵈ, ξ, pulse amplitude, and magnetic‑field orientation reveal two key signatures of strong electronic correlations: (1) a pulse‑dependent shift of the Knight‑shift‑like spectral line, and (2) pronounced temporal asymmetry (non‑mirror‑symmetric echo shapes) that would traditionally be attributed to experimental artefacts. The magnitude and direction of these effects scale with the anisotropy parameters and the interaction range, providing a practical protocol: by measuring the pulse‑dependent shift across different pulse strengths and field orientations, one can extract both the anisotropy of the electronic susceptibility and the spatial extent of the electronic correlations.

The authors validate their approach against experimental observations in unconventional superconductors, spin‑liquid candidates, and FFLO‑type phases, demonstrating that the simulated anomalous echo shapes and multi‑peak spectra reproduce reported data without invoking heating or instrumental errors. They also discuss the inclusion of dissipative terms via a Lindblad master equation as a future extension.

In summary, the work delivers a highly efficient, scalable tool for simulating large, interacting nuclear spin ensembles, establishes a clear theoretical link between pulse‑dependent NMR observables and underlying electronic correlation properties, and opens a new avenue for non‑invasive probing of exotic phases in strongly correlated electron systems.