Antiferromagnetic Heisenberg-Ising ring in the presence of a magnetic flux: Relevance of domain-wall dynamics

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Abstract
We consider a system of charged spinless fermions in a ring governed by the antiferromagnetic Heisenberg-Ising Hamiltonian and in the presence of a magnetic flux. We find that the two broken-symmetry ground states evolve adiabatically with increasing flux with a period corresponding to two flux quanta, while the period of the total spectrum is one flux quantum. This behavior, already observed for this system in the gapless regime [B. Sutherland and B. S. Shastry, Phys. Rev. Lett. 65, 1833 (1990)], is shown to be a natural consequence of the relevant degrees of freedom involved in the low-energy physics of this system: antiferromagnetic domain walls or solitons, with half the charge of the original particles. A space-time approach is introduced to describe the dynamics of these objects, affording a complete topological classification of space-time histories of the system. This allows a physically complete understanding of the ground-state-subspace evolution with increasing flux in the antiferromagnetic broken-symmetry regime. In this case, the flux period doubling can be explained in terms of the Berry’s phase gained by the two degenerate broken-symmetry ground states upon adiabatic switching of the flux.