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Journal of Yangzhou University

DMRG research on a system of quasi-one-dimensional Heisenberg antiferromagnetic chain with symmetry breaking of sublattice

Yongjun Liu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

By using density-matrix renormalization group(DMRG) method,the authors investigate a system of quasi-one-dimensional Heisenberg antiferromagnetic chain with symmetry breaking of sublattice.The ground state energy per unit cell,spin correlation function and staggered susceptibility are calculated.The calculations show that the system exhibits ferrimagnetic properties,although the spin-spin interactions are antiferromagnetic.The results are consistent qualitatively with the conclusion predicted by LIEB-MATTIS theorem and the results calculated by spin-wave theory.

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By using density-matrix renormalization group(DMRG) method,the authors investigate a system of quasi-one-dimensional Heisenberg antiferromagnetic chain with symmetry breaking of sublattice.The ground state energy per unit cell,spin correlation function and staggered susceptibility are calculated.The calculations show that the system exhibits ferrimagnetic properties,although the spin-spin interactions are antiferromagnetic.The results are consistent qualitatively with the conclusion predicted by LIEB-MATTIS theorem and the results calculated by spin-wave theory.
Using density-matrix renormalization group (DMRG) method, we studied the effect of magnetic frustrations due to next-nearest- neighbor bonds in a system of quasi-one-dimensional Heisenberg antiferromagnetic chain but with ferrimagnetic properties. In this paper, the ground state energy per unit cell, spin correlation function and spin gap are calculated. As a result of the frustrations, the quantum disordered phase with the spin gap appears at the spin order-disorder phase transition point αC≈0.412 to α＝1. And in the region of magnetic-order phase, the increasing magnetic frustrations reduce the magnetic order.
Second-order spin-wave expansions are used to compute the ground-state energy and sublattice magnetizations of the quantum one-dimensional Heisenberg ferrimagnet with nearest-neighbor antiferromagnetic interactions and two types of alternating sublattice spins S1>S2.{S}_{1}>{S}_{2}.S1​>S2​. It is found that in the extreme quantum cases (S1,S2){(S}_{1}{,S}_{2})(S1​,S2​)=(1,1/2), (3/2,1), and (3/2,1/2), the estimates for the ground-state energy and sublattice magnetizations differ less than 0.03% for the energy and 0.2% for the sublattice magnetizations from the recently published density-matrix renormalization-group numerical calculations. The reported results strongly suggest that the quantum Heisenberg ferrimagnetic chains give another example of a low-dimensional quantum spin system where the spin-wave approach demonstrates a surprising efficiency.
We study ground-state properties of the Heisenberg frustrated spin chain with interactions up to fourth nearest neighbors by the exact-diagonalization method and the density matrix renormalization group method. We find that ferrimagnetism is realized not only in the case of S=1/2 but also S=1 despite that there is only a single spin site in each unit cell determined from the shape of the Hamiltonian. Our numerical results suggest that a "multi-sublattice structure" is not required for the occurrence of ferrimagnetism in quantum spin systems with isotropic interactions.
The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.