A machine learning analysis of energy and entanglement property of the XYZ quantum spin chain.

A quantum spin chain is a linear arrangement of magnetic moments. Based on competing exchange interaction between the neighboring spins this chain model can allow us to investigate a wide variety of magnetic phenomena with applications ranging from quantum computing to molecular chemistry. From a computational perspective, machine Learning (ML) is a technique based on optimizing a network of interconnected nodes to produce an expected output for any input (in our case the spin chain configuration). We have implemented the convolutional neural network (CNN) ML algorithm to investigate a couple of physical properties, energy, and entanglement, of a fully exchange anisotropic XYZ quantum spin chain. The system was investigated both in the presence of a homogeneous and an inhomogeneous magnetic field. Using computational toolkits (QuSpin for exact diagonalization and ML packages from sci-kit learn), we show that utilizing an ML approach helps to predict the ground state energy of the XYZ system. We will also investigate if our ML analysis can provide insight into the entanglement (negativity) properties of the quantum XYZ spin chain in comparison to the XXZ system.