Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.Haldane conjectures the fundamental difference in the energy spectrum of the Heisenberg antiferromagnetic (HAF) of the spin S chain is that the half-integer and the integer S chain have gapless and gapped energy spectrums, respectively. The ground state (gs) of the HAF spin-1/2 and spin-1 chains have a quasi-long-range and short-range correlation, respectively. We study the effect of the exchange interaction between an HAF spin-1/2 and an HAF spin-1 chain forming a normal ladder system and its gs properties. The inter-chain exchange interaction J⊥ can be either ferromagnetic (FM) or antiferromagnetic (AFM). Using the density matrix renormalization group method, we show that in the weak AFM/FM coupling limit of J⊥, the system behaves like two decoupled chains. However, in the large AFM J⊥ limit, the whole system can be visualized as weakly coupled spin-1/2 and spin-1 pairs which behave like an effective spin-1/2 HAF chain. In the large FM J⊥ limit, coupled spin-1/2 and spin-1 pairs can form pseudo spin-3/2 and the whole system behaves like an effective spin-3/2 HAF chain. We also derive the effective model Hamiltonian in both strong FM and AFM rung exchange coupling limits.

Condensed MatterJan 29, 20231 citation

Random Antiferromagnetic Chain.

Shang-keng Ma, Chandan Dasgupta, Chin‐Kun Hu

Physical Review LettersDec 17, 197913 citations

Antiferromagnetic Linear Chain with Spin 1/2

Takehiko Oguchi

Physical Review LettersSep 15, 19638 citations

A kind of ferromagnetic-antiferromagnetic alternating spin chain equivalent to the mixed spin Heisenberg chain

Jianjun Jiang, Yang Cui-hong, Yongjun Liu

By using the method of exact diagonalization, the properties of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain are investigated. The spin-spin correlation, the sublattice magnetizations, the spin excitation spectrum and the magnetization curve of the model are calculated and compared with the corresponding properties of the mixed spin chain. The results show that the behaviors of the alternating Heisenberg chain are equivalent to those of the mixed spin chain when the ratio of antiferromagnetic to ferromagnetic coupling strength is very small. So, the properties of the mixed spin chain can be analyzed by using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.By using the method of exact diagonalization, the properties of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain are investigated. The spin-spin correlation, the sublattice magnetizations, the spin excitation spectrum and the magnetization curve of the model are calculated and compared with the corresponding properties of the mixed spin chain. The results show that the behaviors of the alternating Heisenberg chain are equivalent to those of the mixed spin chain when the ratio of antiferromagnetic to ferromagnetic coupling strength is very small. So, the properties of the mixed spin chain can be analyzed by using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.

Acta Physica SinicaJan 1, 20120 citations

Anisotropic antiferromagnetic chain in a magnetic field

Tôru Sakai, Minoru Takahashi

Physica B Condensed MatterMay 1, 19985 citations

Numerical evidence of a spin- 1∕2 chain approaching a spin-1 chain

Hsiang-Hsuan Hung, Chang-De Gong

We study the one-dimensional Heisenberg spin- $1∕2$ alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.We study the one-dimensional Heisenberg spin-$1∕2$ alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.

arXiv:cond-mat/0408690Physical Review BFeb 22, 200519 citations

We study the one-dimensional Heisenberg spin-

1∕2

alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and the density matrix renormalization group method, we discuss how the system approaches the AF uniform spin-1 chain under certain conditions. When the ratio of AF to FM coupling strengths, $\ensuremath{\alpha}$ $(\ensuremath{\alpha}={J}_{AF}∕{J}_{F})$, is very small, physical properties of the alternating bond chain such as spin-spin correlation, the string correlation function, and the spin density coincide with those of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with the small $\ensuremath{\alpha}$ limit. In addition, the Haldane gap of the AF uniform spin-1 chain is four times the gap of the system considered.