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1. Excited states in auxiliary field quantum Monte Carlo

   https://doi.org/10.1063/5.0302374  

   Mahajan, Ankit; Sharma, Sandeep; Zhang, Shiwei; Reichman, David R (January 2026, Excited states in auxiliary field quantum Monte Carlo A Mahajan, S Sharma, S Zhang, DR Reichman The Journal of Chemical Physics 164 (4))

   We systematically investigate the calculation of excited states in quantum chemistry using auxiliary field quantum Monte Carlo (AFQMC). Symmetry allows targeting of the lowest triplet excited states in AFQMC based on restricted open-shell determinants, effectively as a ground-state calculation. For open-shell singlet states, excited-state calculations can be stabilized with the appropriate trial states, but their quality can have a larger effect on the accuracy in AFQMC. We find that active space-based configuration interaction trial states are often not sufficient to obtain accurate results. We instead use truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states. We benchmark the performance of these calculations on a set of small and medium molecules and polyacenes, focusing on predominantly single excitations. We find that the AFQMC results, obtained at a per-sample cost scaling of O(N6), are systematically more accurate than those obtained using EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets. In regimes where EOM-CC triples are impractical, these results position AFQMC as a scalable, higher-accuracy complement for low-lying excited states. 

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2. Response properties in phaseless auxiliary field quantum Monte Carlo

   https://doi.org/10.1063/5.0171996  

   Mahajan, Ankit; Kurian, Jo S.; Lee, Joonho; Reichman, David R.; Sharma, Sandeep (November 2023, The Journal of Chemical Physics)

   Unknown (Ed.)

   We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently. 

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3. Quantification of electron correlation for approximate quantum calculations

   https://doi.org/10.1063/5.0119260  

   Yuan, Shunyue; Chang, Yueqing; Wagner, Lucas K. (November 2022, The Journal of Chemical Physics)

   State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions. 

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4. Monte Carlo methods in the manifold of Hartree–Fock–Bogoliubov wave functions

   https://doi.org/10.1063/5.0228450  

   Vitali, Ettore; Rosenberg, Peter; Zhang, Shiwei (October 2024, The Journal of Chemical Physics)

   We explore the possibility of implementing random walks in the manifold of Hartree–Fock–Bogoliubov wave functions. The goal is to extend state-of-the-art quantum Monte Carlo approaches, in particular the constrained-path auxiliary-field quantum Monte Carlo technique, to systems where finite pairing order parameters or complex pairing mechanisms, e.g., Fulde–Ferrell–Larkin–Ovchinnikov pairing or triplet pairing, may be expected. Leveraging the flexibility to define a vacuum state tailored to the physical problem, we discuss a method to use imaginary-time evolution of Hartree–Fock–Bogoliubov states to compute ground state correlations, extending beyond situations spanned by current formalisms. Illustrative examples are provided. 

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5. Investigating the crust of neutron stars with neural-network quantum states

   https://doi.org/10.1038/s42005-025-02015-2  

   Fore, Bryce; Kim, Jane; Hjorth-Jensen, Morten; Lovato, Alessandro (December 2025, Communications Physics)

   Abstract An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm⁻³and 0.1 fm⁻³, matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter. 

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