Persistent currents in 1D rings and the metal-insulator transition under strong long-range Coulomb repulsion

A perturbative approach for large (in comparison with electron overlap and onsite disorder) long-range Coulomb interaction is developed for a 1D ring model. The explicit expression for low-lying energy levels has been obtained. It is shown that in the case of strong repulsive long-range interaction persistent current does not depend exclusively on the filling factor nu =p/q but is extremely sensitive to its denominator q. It also depends on the common factor M of electrons and sites number. In the absence of a common factor (M=1) there exists only one quasiparticle that experiences no strong Coulomb interaction, thus moving freely with bare electron overlap, which provides an unexpectedly large persistent current. For the case of an arbitrary M and a large enough q a system of M weakly interacting quasiparticles has been introduced, which undergoes a metal-insulator transition at unusually small overlap even for a filling factor close to one half. Suppression of the persistent current by disorder is taken into account. Comparison of analytically obtained expressions with the results of numerical calculations shows a reasonable agreement.