Quantum embedding method with transformer neural network quantum states for strongly correlated materials

The neural-network quantum states (NNQS) method is rapidly emerging as a powerful tool in quantum mechanisms. While significant advancements have been achieved in simulating simple molecules using NNQS, the ab initio simulation of complex solid-state materials remains challenging. Here in this work, we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems. Our approach notably reduces the computational problem size while maintaining high accuracy. We have validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems, and have investigated the magnetic ordering and charge density wave state in transition metal compounds. The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.