Neural Networks for Many-Body Physics

Abstract

Solving fundamental equations exactly for larger scale many-body systems is a genuinely intractable problem. The main bottleneck is the “curse of dimensionality,” which arises in either classical or quantum systems. One of the most promising methods nowadays is the use of variational representation based on neural networks, which are known for their extraordinarily high representation power. The current manuscript aims to introduce the concept and application of neural networks to express physics encoded in many-body systems. First, we discuss the application of neural networks for quantum many-body systems. We highlight the property of the ansatz as the ability to capture quantum entanglement, and also introduce the optimization algorithm to realize various processes such as real/imaginary-time evolution. Second, we introduce the exact mapping between classical many-body systems and neural networks, which allow us to apply a global update method for Monte Carlo simulations which drastically speeds up the sampling.