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We evaluate imaginary time density-density correlation functions for atwo-dimensional homogeneous electron gas using the phaseless auxiliary fieldquantum Monte Carlo method. We show that such methodology, once equipped withsuitable numerical stabilization techniques necessary to deal withexponentials, products and inversions of large matrices, gives access to thecalculation of imaginary time correlation functions for medium-sized systems;we present simulations of a number up to 42 correlated fermions in thecontinuum, using up to 300 plane waves as basis set elements. We discuss thenumerical stabilization techniques and the computational complexity of themethodology. We perform the inverse Laplace transform of the obtaineddensity-density correlation functions, assessing the ability of the phaselessauxiliary field quantum Monte Carlo method to evaluate dynamical properties ofmany-fermion systems.

Imaginary Time Correlations for a High-Density two-dimensional Electron Gas