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

TL;DR

This study investigates the ground-state properties of a spin-1/2 tetrameric Heisenberg antiferromagnetic chain, revealing magnetization plateaux, a Haldane-like gap, string order, and hidden symmetry using density matrix renormalization group methods.

Contribution

It uncovers the presence of a Haldane-like phase and hidden $Z_{2}\times Z_{2}$ symmetry in a spin-1/2 tetrameric chain, extending Haldane's scenario to half-integer spins.

Findings

Magnetization plateaux at 0 and 1/4

Existence of a Haldane-like gap

Presence of nonvanishing string order

Abstract

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.