Hierarchy of 1D Electron Models with Long-Range Interaction

Hilton Lazo, Ronald S. Banzon, Cristine Dlr. Villagonzalo

We study the zero-temperature dynamics of the 1D Ising Model with long range interactions. In particular, we focus on the persistence behavior as the strength of the long range interaction is varied. Persistence pertains to those spins that did not flip after some time. We observe that whatever the strength of the long range interaction, the system exhibits blocking where some spins do not flip at all. The system size is also varied to see its effect on these properties.

Seiji Yunoki, Sadamichi Maekawa

DANIEL T. PIERCE

Richard Berkovits, V Frelikher, I. V. Yurkevich +1 more

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.

W. Hansen, D. Schmerek, Chr. Steinebach

Norio Kawakami, Sung-Kil Yang

We review the critical behavior of 1D highly correlated electron systems and 1D quantum many-body systems with long-range interactions. These models exhibit the common universal long-distance properties which are characterized as Luttinger liquids. The microscopic foundation of Luttinger liquids is formulated on the basis of conformal field theory and Bethe-ansatz solutions.