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arXiv:math-ph/0402044 · Journal of Physics A Mathematical and General

Spin of the ground state and the flux phase problem on the ring

Fumihiko Nakano

Published Mar 17, 2004• 0 citations
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Abstract

As a continuation of our previous work, we derive the optimal flux phase which minimizes the ground state energy in the one-dimensional many-particle systems, when the number of particles is odd in the absence of on-site interaction and external potential. Moreover, we study the relationship between the flux on the ring and the spin of the ground state through which we derive some information on the sum of the lowest eigenvalues of one-particle Hamiltonians.

DOI
10.1088/0305-4470/37/13/005

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As a continuation of our previous work, we derive the optimal flux phase which minimizes the ground state energy in the one-dimensional many-particle systems, when the number of particles is odd in the absence of on-site interaction and external potential. Moreover, we study the relationship between the flux on the ring and the spin of the ground state through which we derive some information on the sum of the lowest eigenvalues of one-particle Hamiltonians.
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.