AB effect and persistent current in the Hubbard model

Jian‐Xin Zhu, Z.D. Wang, Li Sheng

By using the Bethe-Yang ansatz within the framework of the tight-binding model, the ground-state energy and the pesistent current in one-dimensional Hubbard rings are calculated in the presence of an AB flux accompanied by a local magnetic field whose direction varies in space. Analytical result are obtained for large-U limit. It is indicated that there usaually exists no short periodicity for the ground-state energy and persistent current due to the effect of the geometric Berry phase even for the case of infinite U. In a special case, the short periodicity retained in the zero-order approximation is broken down by taking into account the first-order energy correction for large but not infinite U. Moreover, it is found that in the strong-coupling limit, the electron-electron interaction suppresses the persistent current, which is in agreement with other numerical calculations.

Jakob Bernasconi

Maria O. Smolkina, I. Yu. Popov, Ashok Chatterjee

Abstract We study the persistent current in a chain of two coupled quantum rings threaded by an Aharonov-Bohm flux in the presence of electron-phonon and Rashba spin-orbit interactions. In the framework of the Holstein-Hubbard model, the equations for ground state energy, persistent current and Drude weight were derived. Obtaining of the expression for the ground state energy allowed us to obtain the persistent current by a conventional way (differentiating). The influence of the magnetic flux and the Rashba spin-orbit interaction on the ground state energy, persistent current and Drude weight was studied numerically.

Jakob Bernasconi

Jian‐Xin Zhu, Z. D. Wang

Based upon a tight-binding model Hamiltonian and by applying the Jordan-Wigner transformation, the Aharonov-Bohm (AB) effect for charged hard-core bosons in one-dimensional (1D) mesoscopic rings is investigated for the first time. By introducing a specific unitary transformation, the energy spectrum and the persistent charge current are analytically derived for ID perfect lattices. Similar to electron systems, it has been found that the energy and persistent current are periodic in AB flux with the period Φ0=hc/q. More interestingly, we have exactly shown that, in the absence of the external AB flux, the charge current can be self-sustained via the AB effect, which is in fact the ground state of the system regardless of the number of hard-core bosons being even or odd.

Gang Su