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Interacting electrons in one dimension: a path integral Monte Carlo study

Path integral Monte Carlo simulations have been carried out for a system of interacting fermionic particles in one dimension. Due to the fact that the sign problem can be completely eliminated for one-dimensional systems, such simulations allow one to obtain accurate energies and particle densities in arbitrary external potentials. Two cases were considered: electrons in the field of a uniform neutralizing background and in an effective field of atoms on a lattice. In the latter case, a clear asymmetry of the charge density distribution of conducting electrons and holes has been observed.