We study the conductance through Aharonov-Bohm finite ladder rings with strongly interacting electrons, modeled by the prototypical $t\text{\ensuremath{-}}J$ model. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux, predicted so far only in chains which are a signature of spin and charge separation. These results open the possibility of observing this peculiar many-body phenomenon in anisotropic ladder systems and in real nanoscopic devices.
We study manifestations of spin-charge separation (SCS) in transport through a tunnel-coupled interacting single-channel quantum ring. We focus on the high-temperature case (temperature
T larger than the level spacing $\mathrm{\ensuremath{\Delta}}$) and discuss both the classical (flux-independent) and interference contributions to the tunneling conductance of the ring in the presence of magnetic flux. We demonstrate that the SCS effects, which arise solely from the electron-electron interaction, lead to the appearance of a peculiar fine structure of the electron spectrum in the ring. Specifically, each level splits into a series of sublevels, with their spacing governed by the interaction strength. In the high-
T limit, the envelope of the series contains of the order of $T/\mathrm{\ensuremath{\Delta}}$ sublevels. At the same time, SCS suppresses the tunneling width of the sublevels by a factor of $\mathrm{\ensuremath{\Delta}}/T$. As a consequence, the classical transmission through the ring remains unchanged compared to the noninteracting case: the suppression of tunneling is compensated by the increase of the number of tunneling channels. On the other hand, the flux-dependent contribution to the conductance depends on the interaction-induced dephasing rate which is known to be parametrically increased by SCS in an infinite system. We show, however, that SCS is not effective for dephasing in the limit of weak tunneling. Moreover, generically, in the almost closed ring, the dephasing rate does not depend on the interaction strength and is determined by the tunneling coupling to the leads. In certain special symmetric cases, dephasing is further suppressed. Similarly to the spinless case, the high-
T conductance shows, as a function of magnetic flux, a sequence of interaction-induced sharp negative peaks on top of the classical contribution.
We calculate the conductance through rings with few sites
L described by the $t\text{\ensuremath{-}}J$ model, threaded by a magnetic flux $\ensuremath{\Phi}$ and weakly coupled to conducting leads at two arbitrary sites. The model can describe a circular array of quantum dots with large charging energy
U in comparison with the nearest-neighbor hopping
t. We determine analytically the particular values of $\ensuremath{\Phi}$ for which a depression of the transmittance is expected as a consequence of spin-charge separation. We show numerically that the equilibrium conductance at zero temperature is depressed at those particular values of $\ensuremath{\Phi}$ for most systems, in particular at half filling, which might be easier to realize experimentally.
The persistent current and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion
U increases, the sign of the current may oscillate depending on the total number of electrons
Ne and the hopping
t between the ring site and the side site. For small hopping
t, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate
U can strongly enhance the persistent current while the hopping
t always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large
U and small
t case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.
Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder. The free energy F(φ) of a metallic ring threaded by an Aharonov-Bohm flux (¯hc/e)φ is a periodic function of φ, with period 2π [1]. The system is said to be diamagnetic if F is minimal for φ = 0, and paramagnetic if F is minimal for φ = π (1/2 flux quantum). A purely one-dimensional (1D) ring with N spinless electrons is diamagnetic if N is even and paramagnetic if N is odd, independent
We study the effects of correlations on a one-dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the Hubbard model and the t - and t - - models. We focus on the dilute limit. Our results suggest the possibility that the persistent current has an anomalous periodicity , where p is an integer in the range ( is the number of particles in the ring and is the flux quantum). We find that this result depends neither on disorder nor on the detailed form of the interaction, while there is still on-site infinite repulsion.