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1. 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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2. 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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3. Emergence of pseudo-time during optimal Monte Carlo sampling and temporal aspects of symmetry breaking and restoration

   https://doi.org/10.1063/5.0135479  

   He, Yang; Lubchenko, Vassiliy (March 2023, The Journal of Chemical Physics)

   We argue that one can associate a pseudo-time with sequences of configurations generated in the course of classical Monte Carlo simulations for a single-minimum bound state if the sampling is optimal. Hereby, the sampling rates can be, under special circumstances, calibrated against the relaxation rate and frequency of motion of an actual physical system. The latter possibility is linked to the optimal sampling regime being a universal crossover separating two distinct suboptimal sampling regimes analogous to the physical phenomena of diffusion and effusion, respectively. Bound states break symmetry; one may thus regard the pseudo-time as a quantity emerging together with the bound state. Conversely, when transport among distinct bound states takes place—thus restoring symmetry—a pseudo-time can no longer be defined. One can still quantify activation barriers if the latter barriers are smooth, but simulation becomes impractically slow and pertains to overdamped transport only. Specially designed Monte Carlo moves that bypass activation barriers—so as to accelerate sampling of the thermodynamics—amount to effusive transport and lead to severe under-sampling of transition-state configurations that separate distinct bound states while destroying the said universality. Implications of the present findings for simulations of glassy liquids are discussed. 

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4. Benchmarking the semi-stochastic CC( P ; Q ) approach for singlet–triplet gaps in biradicals

   https://doi.org/10.1063/5.0100165  

   Chakraborty, Arnab; Yuwono, Stephen H.; Deustua, J. Emiliano; Shen, Jun; Piecuch, Piotr (October 2022, The Journal of Chemical Physics)

   We recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet–triplet gaps of biradical systems using methylene, (HFH)−, cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples. 

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5. Interaction-driven spontaneous ferromagnetic insulating states with odd Chern numbers

   https://doi.org/10.1038/s41535-023-00544-z  

   Mai, Peizhi; Huang, Edwin W.; Yu, Jiachen; Feldman, Benjamin E.; Phillips, Philip W. (December 2023, npj Quantum Materials)

   Abstract Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence ± (2 N  + 1). These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction. 

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