Deep learning calculation for many-body electronic structure in condensed matter

The accurate solution of the many-body electronic structure problem is a key scientific challenge for understanding and predicting the physical properties of materials. Traditional computational methods, however, have long been constrained by a fundamental trade-off between accuracy and efficiency. This review introduces an emerging first-principles computational approach that integrates deep learning with quantum Monte Carlo methods. Its core principle is to construct highly expressive and systematically improvable many-body wavefunction ansatzes using deep neural networks. These wavefunctions are then optimized via the variational Monte Carlo method to approximate the exact solution of the many-electron Schrödinger equation. Results have shown that this method can treat diverse physical systems, including both molecules and periodic solids, in a unified and highly accurate manner. Moreover, it demonstrates unique advantages in tackling strongly correlated topological phases. The deep learning quantum Monte Carlo method provides a powerful and versatile approach for understanding condensed matter phenomena, predicting material properties with high-precision, and discovering novel quantum phases of matter, thus opening a new avenue in condensed matter physics.