Modeling strongly correlated states with auxiliary-field quantum Monte Carlo

Strong correlation in interacting quantum systems can give rise to emergent physical phenomena and remarkable chemical reactivity. However, accurate numerical modeling of strongly correlated states in relevant lattice models, molecules, or materials with approximate many-body techniques is challenging, typically due to the presence of competing or even frustrated orders (e.g. magnetic phases) and the intractable growth of Hilbert space size with the number of particles. In this regime, nonperturbative and stochastic methods have many advantages, and auxiliary-field quantum Monte Carlo (AFQMC) has emerged as a prominent technique in many fields of chemistry and physics. After providing a detailed overview of the AFQMC methodology, including a historical overview and with particular emphasis on the constrained-path and phaseless constraints, I will share recent developments from my research group related to trial wavefunction exploration and studies of strongly correlated molecular systems.