Hartree-Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree-Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree-Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree-Fock result obtained in the local approximation, in particular the persistent current behaving like I ∝ L^{- 1 - α}, where L is the ring length and α > 0 is the power depending only on the electron-electron interaction. Finally, we use the Hartree-Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree-Fock results.