Extending Quantum Spin Dynamics Across Time and Space Using Neural Networks

Obtaining the spectrum and dynamical responses of quantum materials is essential for understanding their physical properties. The dynamical responses of some simple quantum magnetic systems can be calculated analytically; however, this is not possible for many complex many-body systems. While numerical methods like Time-Dependent Density Matrix Renormalization Group (tDMRG) exist, they propogate errors over long time steps and face computational complexity at large system sizes. In this project, we employ machine learning algorithms to enhance the dynamical spin correlations in both time and space with improved resolution. Our models are trained using tDMRG data simulated for the XXZ model on a finite-size 1D lattice. We validate our results against those from analytical calculations using the Bethe Ansatz and Exact Diagonalization. Through this method, we aim to analyze other strongly interacting many-body systems lacking analytical solutions, enhancing our understanding of dynamical spin correlations with greater resolution, especially for systems approaching the thermodynamic limit.