Boundary Green's Function for Spin-Incoherent Interacting Electrons in 1D
Recently the properties of one-dimensional (1D) strongly interacting, very low-density electrons in the spin-incoherent regime have been under intense study. For sufficiently low densities the potential energy dominates the kinetic energy, making the electrons form a Wigner crystal with an exponentially small spin exchange energy. One can then easily reach the spin-incoherent regime where
the exchange energy is much smaller than the temperature. The physics of the spin-incoherent regime has been addressed using Bethe's Ansatz and a bosonized path integral approach, revealing that the spin incoherence dramatically influences the correlations of charge excitations. We here introduce a bosonization scheme for strongly interacting electrons, allowing us to generalize the description to account for the presence of a boundary. By calculating the exact single-electron Green's function we find that the charge sector power-law scaling is highly sensitive to the bound-
ary, strongly modifying the tunneling of electrons close to it. Our approach also allows for a detailed description of the crossover between boundary and bulk regimes.