Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo

Abstract

Recent developments in selected configuration interaction methods have led to increased interest in using multi-Slater trial wave functions in various quantum Monte Carlo (QMC) methods. Here we present an algorithm for calculating the local energy of a multi-Slater wave function in orbital space QMC. For an ab initio Hamiltonian, our algorithm has a cost scaling of $O(n^5+n_c)$, as opposed to the $O(n^4{n}_c)$ scaling of existing orbital space algorithms, where $n$ is the system size, and $n_c$ is the number of configurations in the wave function. We present our method using variational Monte Carlo calculations with the Jastrow multi-Slater wave function, although the formalism should be applicable for auxiliary field quantum Monte Carlo. We apply it to polyacetylene and demonstrate the possibility of using a much larger number of configurations than possible using existing methods.

arXiv comment10 pages, 3 figures

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• Self-Refinement of Auxiliary-Field Quantum Monte Carlo via Non-Orthogonal Configuration Interaction
• Fixed and partial-node approximations in Slater determinant space for molecules
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