  We study the zero-temperature phase diagram of a dissipationless and
disorder-free Josephson junction chain. Namely, we determine the critical
Josephson energy below which the chain becomes insulating, as a function of the
ratio of two capacitances: the capacitance of each Josephson junction and the
capacitance between each superconducting island and the ground. We develop an
imaginary-time path integral Quantum Monte-Carlo algorithm in the charge
representation, which enables us to efficiently handle the electrostatic part
of the chain Hamiltonian. We find that a large part of the phase diagram is
determined by anharmonic corrections which are not captured by the standard
Kosterlitz-Thouless renormalization group description of the transition.
