Electron correlation effects in low dimensional periodic systems

We explore the role of electron correlation in quasi-one-dimensional quantum wires as the range of the interaction potential is changed and their thickness is varied by performing exact quantum Monte Carlo simulations at various electronic densities. In the case of unscreened interactions with a long-range $1/x$ tail there is a crossover from a liquid to a quasi-Wigner crystal state as the density decreases. When this interaction is screened, quasi-long-range order is prevented from forming, although a significant correlation with $4{k}_{F}$ periodicity is still present at low densities. At even lower electron concentration, exchange is suppressed and the electrons behave like spinless fermions. Finally, we study the effect of electron correlations in the double quantum wire experiment [Steinberg et al., Phys. Rev. B 73, 113307 (2006)] by introducing an accurate model for the screening in the experiment and explicitly including the finite length of the system in our simulations. We find that decreasing the electron density continuously drives the system from a liquid to a state with quite strong $4{k}_{F}$ correlations. This crossover takes place around $22\text{ }\ensuremath{\mu}{\text{m}}^{\ensuremath{-}1}$, near the density where the electron localization occurs in the experiment. The charge and spin velocities are also in good agreement with the experimental findings in the proximity of the crossover. We argue that correlation effects play an important role at the onset of the localization transition.We explore the role of electron correlation in quasi-one-dimensional quantum wires as the range of the interaction potential is changed and their thickness is varied by performing exact quantum Monte Carlo simulations at various electronic densities. In the case of unscreened interactions with a long-range $1/x$ tail there is a crossover from a liquid to a quasi-Wigner crystal state as the density decreases. When this interaction is screened, quasi-long-range order is prevented from forming, although a significant correlation with $4{k}_{F}$ periodicity is still present at low densities. At even lower electron concentration, exchange is suppressed and the electrons behave like spinless fermions. Finally, we study the effect of electron correlations in the double quantum wire experiment [Steinberg et al., Phys. Rev. B 73, 113307 (2006)] by introducing an accurate model for the screening in the experiment and explicitly including the finite length of the system in our simulations. We find that decreasing the electron density continuously drives the system from a liquid to a state with quite strong $4{k}_{F}$ correlations. This crossover takes place around $22\text{ }\ensuremath{\mu}{\text{m}}^{\ensuremath{-}1}$, near the density where the electron localization occurs in the experiment. The charge and spin velocities are also in good agreement with the experimental findings in the proximity of the crossover. We argue that correlation effects play an important role at the onset of the localization transition.

arXiv:0803.1211Physical Review BOct 6, 200845 citations

1/x

tail there is a crossover from a liquid to a quasi-Wigner crystal state as the density decreases. When this interaction is screened, quasi-long-range order is prevented from forming, although a significant correlation with

4{k}_{F}

periodicity is still present at low densities. At even lower electron concentration, exchange is suppressed and the electrons behave like spinless fermions. Finally, we study the effect of electron correlations in the double quantum wire experiment [Steinberg et al., Phys. Rev. B 73, 113307 (2006)] by introducing an accurate model for the screening in the experiment and explicitly including the finite length of the system in our simulations. We find that decreasing the electron density continuously drives the system from a liquid to a state with quite strong

4{k}_{F}

correlations. This crossover takes place around $22\text{ }\ensuremath{\mu}{\text{m}}^{\ensuremath{-}1}$, near the density where the electron localization occurs in the experiment. The charge and spin velocities are also in good agreement with the experimental findings in the proximity of the crossover. We argue that correlation effects play an important role at the onset of the localization transition.