Quantum vortex melting and superconductor insulator transition in a 2D Josephson junction array in a perpendicular magnetic field via diffusion Monte Carlo

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In this study, we simulated a quantum rotor model describing a Josephson junction array (JJA) in the phase representation at zero temperature in a perpendicular magnetic field (in units of ) on a square lattice with spacing a for . The superconductor-insulator transition (SIT) is tuned by the ratio of charging energy to Josephson coupling, U/J. Abrupt drops in the magnetization values were observed in the bigger lattices at certain values of B and U/J caused by the formation of vortices. Increasing U/J at a fixed B field causes quantum vortex melting. The magnetization drops to zero around indicating SIT. For B = 0.1 the SIT occurs without an intermediate vortex state and the magnetization scales as , whereas for B = 0.4 the scaling is during the vortex melting. For B between 0.1 and 0.4 the scaling is not clear. We used the diffusion Monte Carlo (DMC) method with a guiding wavefunction optimized using the variational Monte Carlo (VMC) method. The ground state energy is calculated easily in DMC and its error estimates were generally smaller than , both with and without the guiding wavefunction. Quantities like magnetization and vorticity that do not commute with the Hamiltonian were calculated using an efficient forward walking algorithm. Their estimates are affected severely in absence of the guiding wavefunction. With the guiding wavefunction, errors for the magnetization were generally less than and going up to percent around the phase transition from the Meissner to the vortex state, and without the guiding wavefunction errors were generally higher than and going up to around the critical point.