Hubbard ring: currents induced by change of magnetic flux

TL;DR

This paper studies how changing magnetic flux in a quantum Hubbard ring induces currents, revealing how electron correlations influence current dynamics and implications for quantum motor design.

Contribution

It demonstrates that the time-dependent current reflects electron correlations and proves flux change independence for certain Hubbard models after the final flux is reached.

Findings

Current after flux change is independent of prior flux variation in the infinite on-site repulsion Hubbard model.

The induced current depends solely on initial equilibrium state and final flux value.

Results have implications for quantum motor design using ring-shaped optical lattices.

Abstract

We investigate currents in a quantum ring threaded by a magnetic flux which can be varied in an arbitrary way from an initial value $\phi_i$ at time $t_i$ to a final value $\phi_f$ at time $t_f$. Dynamics of electrons in the ring is described by the Hubbard and the extended Hubbard models. We demonstrate that time dependence of the induced current bears information on electron correlations. In the case of the Hubbard model with infinite on--site repulsion we prove that the current for $t>t_f$ is independent of the flux variation before $t_f$. Additionally, this current is fully determined by a solution of the initial equilibrium problem and the value of $\phi_f$. Apart from mesoscopic rings our results pose important implications for designing of quantum motors built out as the ring--shaped optical lattice.