Variational Monte Carlo study of two dimensional charged bosons

We studied the ground state properties of 2D charged Bosons interacting via Coulomb potential using the Variational Monte Carlo method. We start with the paper of McMillan [1] in which there are 3D Bosons interacting via Lennard-Jones potential. We calculate ground state energy and pair distribution function of the system and our results are compared with the original work. We also reproduce the paper of Liu et al. [2] and study the 2D Bosons interacting with the same potential. Our results are compared with the original work. In order to evaluate long-range potentials in periodic systems we introduce Ewald summation method for 2D system and Natoli-Ceperley method which evaluates potentials optimally. We compare our Natoli-Ceperley results with the Holzmann et al. [3]. We also investigate 2D charged Boson system interacting via Coulomb potential using the RPA pseudo potential. Our results are compared with de Palo et al. [4]. We try to optimize the wave function further introducing a Kinetic Energy projection to the original RPA wave function. We show that it is very difficult to optimize it further since it is a very good wave function.