Magnetization plateaux, Haldane-like gap, string order and hidden symmetry in a spin-1/2 tetrameric Heisenberg antiferromagnetic chain

Details Magnetization plateaux, Haldane-like gap, string order and hidden symmetry in a spin-1/2 tetrameric Heisenberg antiferromagnetic chain Magnetization plateaux, Haldane-like gap, string order and hidden symmetry in a spin-1/2 tetrameric Heisenberg antiferromagnetic chain

2008-08-31

arxiv.org/abs/0809.0093v1

Phys. Rev. B 78, 104416 (2008) (Editors' suggestions)

Physics

Condensed Matter

Strongly Correlated Electrons

11pages, 7 figures

Scientific paper

10.1103/PhysRevB.78.104416

The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF$_{1}$-AF$_{2}$-AF$_{1}$% -F (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density matrix renormalization group method. Two plateaux of magnetization $m$ are found at $m=0$ and 1/4% . It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped states have a nonvanishing string order, which measures a hidden symmetry in the system. By a dual transformation, the string order is transformed into a ferromagnetic order and the hidden symmetry is unveiled to be a $Z_{2}\times Z_{2}$ discrete symmetry, which is fully broken in the gapped states. This half-integer spin Heisenberg AF chain is in a Haldane-like phase, suggesting that the present findings extend the substance of Haldane's scenario. A valence-bond-solid state picture is also proposed for the gapped states.

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