Investigating Frustrated Magnetism With Symmetry Aware Neural Networks

This thesis concerns the development of neural network models for understanding magnetism in quantum many body systems. Chapter 1 discusses the quantum many body problem and the outstanding difficulty of modeling many-body physics. Chapter 2 introduces spin models, frustrated magnetism, quantum spin liquids, and some of the numerical approaches used to solve these problems. Chapter 3 describes the neural quantum state approach, a novel method for encoding the wavefunction of a quantum many body system. Chapter 4 provides some background material on group theory, lattice symmetry groups, and classical and quantum orders. These are techniques that, in combination with symmetry-resolved neural networks, can be used to provide novel analysis on quantum spin liquids and other strongly-correlated quantum many body phases. Chapter 5 introduces the group convolutional neural network (GCNN) for building symmetry-resolved neural quantum states and shows simulation results on various Heisenberg models. Chapter 6 describes some computational software for implementing GCNNs as part of the software package NetKet. Chapter 7 is a bit of a thematic departure, and describes developing NQS methods to model quantum systems in the thermodynamic limit. Chapter 8 provides a summary and suggests avenues for future research