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

TY - JOUR

T1 - Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods

AU - Blunt, Nick S.

AU - Alavi, Ali

AU - Booth, George H.

PY - 2018/8/9

Y1 - 2018/8/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85051526197&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.98.085118

DO - 10.1103/PhysRevB.98.085118

M3 - Article

AN - SCOPUS:85051526197

SN - 2469-9950

VL - 98

JO - Physical Review B

JF - Physical Review B

IS - 8

M1 - 085118

ER -