Numerical algorithm for the calculation of the ground states in the U_QSU(2) symmetric spin 1/2 Heisenberg chain

Ground-state magnetization curves of ferrimagnetic Heisenberg chains of alternating spins S and s are numerically investigated. Calculating several cases of $(S,s),$ we conclude that the spin- $(S,s)$ chain generally exhibits $2s$ magnetization plateaus even at the most symmetric point. In the double- or more-plateau structure, the initial plateau is generated on a classical basis, whereas the higher ones are based on a quantum mechanism.Ground-state magnetization curves of ferrimagnetic Heisenberg chains of alternating spins S and s are numerically investigated. Calculating several cases of $(S,s),$ we conclude that the spin-$(S,s)$ chain generally exhibits $2s$ magnetization plateaus even at the most symmetric point. In the double- or more-plateau structure, the initial plateau is generated on a classical basis, whereas the higher ones are based on a quantum mechanism.

arXiv:cond-mat/0005248Physical review. B, Condensed matterAug 1, 200045 citations

Study of the ground state of the one-dimensional Heisenberg spin-1/2 chain

K.R. de Ruiter

We discuss the ground state of the Heisenberg spin-1/2 chain in one dimension, considering nearest neighbor interactions. In the thermodynamic limit the energy is calculated analytically in several ways. We start by applying the Bethe ansatz to calculate the exact ground state energy of the XXX Heisenberg model. Next we study small perturbations of the spin anisotropy, the parameter for the interaction in the z-direction for the XXZ model, by applying time-independent perturbation theory. In addition we expand an exact integral expression of the energy of the XXZ model around the spin anisotropy in the thermodynamic limit. The results are compared to numerical solutions, which are obtained by means of exact diagonalization up to twelve lattice sites. We find that for ten or more lattice sites the numerics agree well with the expectation from the analytical calculations. Finally the concept of integrability is discussed in the context of the Heisenberg model.We discuss the ground state of the Heisenberg spin-1/2 chain in one dimension, considering nearest neighbor interactions. In the thermodynamic limit the energy is calculated analytically in several ways. We start by applying the Bethe ansatz to calculate the exact ground state energy of the XXX Heisenberg model. Next we study small perturbations of the spin anisotropy, the parameter for the interaction in the z-direction for the XXZ model, by applying time-independent perturbation theory. In addition we expand an exact integral expression of the energy of the XXZ model around the spin anisotropy in the thermodynamic limit. The results are compared to numerical solutions, which are obtained by means of exact diagonalization up to twelve lattice sites. We find that for ten or more lattice sites the numerics agree well with the expectation from the analytical calculations. Finally the concept of integrability is discussed in the context of the Heisenberg model.

Jan 1, 20180 citations

A new method to solve the S=1/2 Heisenberg spin chain

Nian Lin, Yu, Z.

Jan 1, 19930 citations

A Numerical Study of Spin-1/2 Alternating Antiferromagnetic Heisenberg Chains

KIYOMI OKAMOTO

Jan 1, 19860 citations

Ground-state magnetization curves of ferrimagnetic Heisenberg chains of alternating spins S and s are numerically investigated. Calculating several cases of

(S,s),

we conclude that the spin-

(S,s)

chain generally exhibits

2s

magnetization plateaus even at the most symmetric point. In the double- or more-plateau structure, the initial plateau is generated on a classical basis, whereas the higher ones are based on a quantum mechanism.