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Physics Letters A

Properties of spin-1/2 antiferromagnetic Heisenberg chain with dimerization and exchange anisotropy

Qing Jiang, X.Y. Chen, Xuefan Jiang

Published Sep 1, 2001• 5 citations
Publisher
DOI
10.1016/s0375-9601(01)00523-0

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The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J') alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J'\ensuremath{\rightarrow}-\ensuremath{\infty}, J>0), the dimerized spin-1/2 AFHC (J'\ensuremath{\simeq}J>0), and the uniform spin-1/2 AFHC (J'=J>0) continuously. The string order introduced by den Nijs--Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J'. It is at a maximum for J'=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.
Spontaneous dimerization is found in the S=12S=\frac{1}{2}S=21​ isotropic Heisenberg antiferromagnetic chain with competing nearest- and next-nearest-neighbor exchange, $\frac{{J}_{2}}{{J}_{1}}\ensuremath{\gtrsim}\frac{1}{6}$, and results from the same umklapp processes that lead to the N\'eel state when easy-axis exchange anisotropy is present. Spontaneous and externally induced dimerizations are contrasted.
Using density matrix renormalization group calculations, ground state properties of the spin–1 Heisenberg chain with exchange and quadratic single-ion anisotropies in an external field are studied, for special choices of the two kinds of anisotropies. In particular, the phase diagram includes antiferromagnetic, spin-liquid (or spin-flop), IS2, and supersolid (or biconical) phases. Especially, new features of the spin-liquid and supersolid phases are discussed. Properties of the quantum chains are compared to those of corresponding classical spin chains.