Aharonov-bohm Effect in Luttinger Liquid and Beyond*

In systems with the spin-charge separation, the period of the Aharonov-Bohm (AB) oscillation becomes half of the flux quantum. This effect is at least related to the fact that for the creation of the holons (spinons) are needed two electrons. The effect is illustrated on the example of the Hubbard Hamiltonian with the aid of the bosonization including topological numbers and exists also in the Luttinger liquid on two chains. The relation to a fractional 1/N AB effect, which can be associated with a modified Luttinger liquid, is discussed. In practically all 1D strongly-correlated electron systems there exists the phenomenon known as ”spin-charge” separation [1]. It was also recently argued[2] that the spin charge separation is not only inherent to 1D, but also occurs in the two-dimensional systems related to HTSC. The degrees of freedom associated with the single electron are split into two independent spin and charge degrees of freedom associated with single particle gapless excitations: spinons and holons as in 1D Luttinger liquid[3]. We show [4]that the properties of strongly-correlated systems are associated with a new type of AB effect, namely, the period of the AB effect decreases and becomes half of the period of the AB oscillations for the free electrons[5]. This is valid for all systems where the spin-charge separation exists. The spinon, as well as the holon exci-