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Physica A Statistical Mechanics and its Applications

Persistent currents in interacting lattice models

Michael Abraham, Richard Berkovits

Published Nov 1, 1993• 8 citations
Publisher
DOI
10.1016/0378-4371(93)90555-i

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Persistent current and Drude weight of one-dimensional interacting fermions on imperfect ring from current lattice density functional theory

Akinlolu Akande, Stefano Sanvito

We perform a numerical study of interacting one-dimensional Hubbard rings with a single impurity potential and pierced by a magnetic flux. Our calculations are carried out at the level of current lattice density functional theory (CLDFT) for the Hubbard model and compared to known results obtained in the thermodynamical limit from the Bethe ansatz. In particular, we investigate the effects of disorder and Coulomb interaction on the persistent current (PC) and the Drude weight. It is found that CLDFT is able to accurately describe qualitative and quantitative features of these ground state properties in the presence of disorder and electronic interaction. When the impurity potential is switched off, the CLDFT approach describes well the velocity of the Luttinger liquid excitations as a function of both interaction strength and electron filling. Then, when the impurity scattering potential is finite, we find the PC to vanish as [Formula: see text] for large L and independent on the strength of the scattering potential, in good agreement with Luttinger liquid theory.

Journal of Physics Condensed Matter•Sep 8, 2016•1 citation
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.
We perform a numerical study of interacting one-dimensional Hubbard rings with a single impurity potential and pierced by a magnetic flux. Our calculations are carried out at the level of current lattice density functional theory (CLDFT) for the Hubbard model and compared to known results obtained in the thermodynamical limit from the Bethe ansatz. In particular, we investigate the effects of disorder and Coulomb interaction on the persistent current (PC) and the Drude weight. It is found that CLDFT is able to accurately describe qualitative and quantitative features of these ground state properties in the presence of disorder and electronic interaction. When the impurity potential is switched off, the CLDFT approach describes well the velocity of the Luttinger liquid excitations as a function of both interaction strength and electron filling. Then, when the impurity scattering potential is finite, we find the PC to vanish as [Formula: see text] for large L and independent on the strength of the scattering potential, in good agreement with Luttinger liquid theory.