ML Extension of Spin Correlation in Space and Time

Obtaining the spectrum and dynamical responses of quantum materials can

be fundamental to microscopic understanding of their physical properties. For

quantum magnetism, the dynamical responses of certain simple systems can be

calculated analytically; however, this cannot be acquired for numerous complex

many-body systems. While numerical methods, such as exact diagonalization

and density matrix renormalization group (DMRG), exist for such systems, the time evolution algorithms often propagate errors that depreciate the accuracy of the

spectra at long time and space intervals. In addition, the computational cost of

these numerical methods drastically increases with the size of the system, preventing us from studying systems approaching the thermodynamic limit. In this

project, we employ machine learning algorithms to extend the dynamical spin

correlations in both temporal and spatial dimensions with improved resolution.

We train the models using Time-dependent Density Matrix Renormalization

Group (tDMRG) simulated for XXZ model on a finite-size one-dimensional lattice. We benchmark our machine learning obtained spin dynamical correlation

results against those obtained from analytical calculations of solvable models

such as the XXZ model. After assessing the accuracy of our machine learning

model, we hope to analyze other strongly interacting many-body systems that

do not have an analytical solution using this method. This method aims to

enhance the understanding of the dynamical spin correlation with much higher

resolution, and for systems approaching the thermodynamic limit.