Shou-Shu Gong and Gang Su *
College of Physical Sciences, Graduate University of Chinese Academy of Sciences,
P.O. Box 4588, Beijing 100049, People’s Republic of China
(Received 7 May 2008; revised manuscript received 4 July 2008; published 18 September 2008)

Abstrat:

The ground-state properties of a spin S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF₁-AF ₂-AF₁-F (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density-matrix renormalization-group method. Two plateaus 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 ×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.