Nonlinear light cone spreading of correlations in a triangular quantum magnet: a hard quantum simulation target

Dynamical correlations of quantum many-body systems are typically analyzed in the momentum space and frequency basis. However, quantum simulators operate more naturally in real space, real time settings. Here we analyze the real-space time-dependent van Hove spin correlations $G(r,t)$ of the 2D triangular antiferromagnet KYbSe$_2$ as obtained from high-resolution Fourier-transformed neutron spectroscopy. We compare this to $G(r,t)$ from five theoretical simulations of the well-established spin Hamiltonian. Our analysis reveals non-linear sub-ballistic low-temperature transport in KYbSe$_2$ which none of the current state-of-the-art numerical or field-theoretical methods reproduce. Our observation signals an emergent collective hydrodynamics, perhaps associated with the quantum critical phase of a quantum spin liquid, and provides an ideal benchmark for future quantum simulations.