Quantum Monte Carlo
Quantum Monte Carlo (QMC) is an umbrella term that refers to computational methods using stochastic sampling in some form to study interacting quantum systems.
A key characteristic of the quantum many-body problem is the high dimensionality of the Hilbert space involved. QMC methods thus have an integral role in CCQ activities.
QMC at CCQ is anchored by both methodological innovations and software developments. It spans a wide range of algorithms:
- AFQMC: formulating the solution of the Schrödinger equation directly as random walks in a manifold of Slater determinants (auxiliary-field quantum Monte Carlo, or AFQMC);
- NQS/VMC: evaluating expectation values of a given many-body wave function ansatz and optimizing with respect to the neural network and/or many parameters (variational Monte Carlo, often used in combination with neural quantum states – NQS – and machine learning) – see `Machine Learning’ project.
- DiagMC: evaluating by sampling the successive terms of perturbation theory and summing this series to reach strong-coupling regimes (diagrammatic Monte Carlo).
- Monte Carlo sampling methods to solve local quantum impurity problems which are central to dynamical mean-field theory (DMFT) and quantum embedding methods.
The QMC effort connects broadly to multiple application domains including condensed matter physics, ultracold atoms in AMO physics, quantum chemistry, and materials physics. It is driven by solving outstanding problems ranging from understanding model systems for exotic quantum states to ab initio and predictive computations in molecules and solids.
Project Leaders: Shiwei Zhang, Miguel Morales
Project Scientists: Leonardo dos Anjos Cunha, Brandon K. Eskridge, Thomas Hahn, Conor Smith, Olivier Parcollet, Agnes Valenti, Zhou-Quan Wan, Lukas Weber, Nils Wentzell, Yueqing Chang