Dynamical imaginary-time correlations from auxiliary fields quantum Monte Carlo

Quantum Monte Carlo (QMC) simulations of many body fermionic systems are considerably complicated by the well known sign problem. Although very accurate approximation schemes have been developed for the calculation of static properties, like structure functions and energy, the possibility of extending such methodologies to the investigation of dynamical properties is still largely unexplored. Recently, a number of innovative QMC methods have been conceived which map the imaginary time evolution into a random walk in the abstract manifold of Slater determinants. In such approaches the sign problem is not circumvented and still requires approximations, but emerges in a different - and hopefully easier to handle - way. We have focused on the phaseless auxiliary Fields QMC method (AFQMC), developed by Shiwei Zhang. Generalizing the formal manipulations suggested by Assaad et al., we propose a practical scheme to evaluate dynamic correlation functions in imaginary time, giving access to the study of excitations and response functions of interacting fermionic systems. We have explored systematically the effects of the phaseless approximation, underlying the AFQMC technique and its dynamical generalization, via the study of exactly solvable simple models, comparing AFQMC predictions with exact solutions. We will present also results about a two-dimensional electron liquid, providing comparisons with other QMC techniques.