Ground State Properties for a Bose Gas Within a Periodic, Multi-Rods Structure

We calculate the ground state (gs) energy and the static structure factor at zero temperature of an interacting Bose gas confined by a one-dimensional, periodic, multi-rods structure created by an external Kronig-Penney potential. We employ the Diffusion Monte Carlo (DMC) method to solve the Schrödinger equation exactly up to a statistical error. The gs energy is compared with the results previously obtained using the Variational Monte Carlo method (VMC), as well with the results obtained using the Mean-Field theory approximation by solving analytically the Gross-Pitaevskii equation. In the limit of zero external potential, we recover the results for the well-known Lieb-Liniger model [1]. For nonzero external potential, we find a phase transition from the superfluid state to a Mott insulator state as the lattice height increases. [1] E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).