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Bulletin of the American Physical Society

Auxiliary-field based trial wave functions in quantum Monte Carlo simulations

Chia‐Chen Chang, Brenda M. Rubenstein, Miguel A. Morales

Published Mar 16, 2016• 0 citations
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Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.

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Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths, and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multideterminant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis-set full configuration interaction energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite--size solid-state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis-set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wave function than DMC while simultaneously exhibiting a much larger basis-set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.