Auxiliary Field Diffusion Monte Carlo Methods: From Baryonic Matter to Quantum Wells
Quantum Monte Carlo methods have proven to be very successful in predicting the behaviour of complex many-body systems. One of the most interesting features of this algorithm is the flexibility and portability across different problems. In this talk I will briefly illustrate the basics of the method, and show how recent progress achieved in the capability of treating complex Hamiltonians used in nuclear physics, branches in an efficient algorithm to treat certain many-electron systems of technical interest.
The focus will be on the so-called Auxiliary Field Diffusion Monte Carlo method (AFDMC). AFDMC provides an efficient way to compute the properties of many-nucleon systems described by realistic interactions like the Argonne AVX potential, avoiding in principle the problem of the exponentially growing computational cost as a function of the number of nucleons at the cost of introducing a set of auxiliary variables. Recent applications of this algorithm include, for instance, computations of the equation of state of baryonic matter, of great interest for understanding the structural properties of compact stars. On the other hand, a two-dimensional system of electrons, as it can be obtained in semiconductor quantum wells, when subject to a transverse electric field can be described in terms of a spin-orbit like Hamiltonian (the Rashba and Dresselhaus potentials). The possibility of controlling the spin polarization of this system is essential in building spintronics applications. An analog of the AFDMC algorithm can be directly applied to the study of such systems, and some results will be presented.