The Lognormal Distribution and Quantum Monte Carlo Data

Abstract

AbstractQuantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method entails reconstructing the probability distribution of a set of data, with given mean and variance, that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation. In doing so, we perform a numerical evaluation of the renormalized sum of lognormal random variables. This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.