Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral 
functions in quantum Monte Carlo methods

Blunt, N.; Alavi, A.; Booth, G.

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Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods

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Alavi, A.
Department Electronic Structure Theory (Ali Alavi), Max Planck Institute for Solid State Research, Max Planck Society;

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Blunt, N., Alavi, A., & Booth, G. (2018). Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods. Physical Review B, 98(8): 085118.

Cite as: https://hdl.handle.net/21.11116/0000-000E-D340-B

Abstract

In this paper, we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of nonlinear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected full configuration interaction quantum Monte Carlo (KP-FCIQMC) approach, which was recently introduced to allow efficient, stochastic calculation of dynamical properties. This requires the solution of a sampled effective Hamiltonian, resulting in a nonlinear operation on these stochastic variables. We investigate the probability distribution of this eigenvalue problem to study both stochastic errors and systematic biases in the approach, and demonstrate that such errors can be significantly corrected by moving to a more appropriate basis. This is lastly expanded to include consideration of the correlation function quantum Monte Carlo (QMC) approach of Ceperley and Bernu, showing how such an approach can be taken in the full configuration interaction QMC (FCIQMC) framework.