Discovering correlated fermions using quantum Monte Carlo

Abstract

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.

submission to RoPP review issue

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• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
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• An efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations
• Large Scale Parallelization in Stochastic Coupled Cluster
• Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo
• Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation
• Ground-state properties of the narrowest zigzag graphene nanoribbon from quantum Monte Carlo and comparison with density functional theory
• Binding and excitations in Si${}_x$H${}_y$ molecular systems using quantum Monte Carlo
• Prediction for the singlet-triplet excitation energy for the spinel MgTi${}_2$O${}_4$ using first-principles diffusion Monte Carlo
• An efficient hybrid orbital representation for quantum Monte Carlo calculations
• Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification
• Assessing many-body methods on the potential energy surface of the (H${}_2$)${}_2$ hydrogen dimer
• Diffusion Monte Carlo study of a spin-imbalanced two-dimensional Fermi gas with attractive interactions
• The Future of the Correlated Electron Problem