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Journal of Yangzhou University

The ground state of the 1/5-doped antiferromagntic spin chain

Yongjun Liu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

By density-matrix renormalization group method,the 1/5-doping effect on the spin-1/2 Heisenberg antiferromagnetic chain is investigated.It is shown that adding side spins can weaken the correlations between near-neighbor spins while strengthen those between long-range spins.Because of the broken of sublattice symmetry by side spins,the ferromagnetic and the antiferromagnetic long range orders can coexist in the ground state.Side spins can lower the quantum fluctuations,and the effect will weaken as the increasing of interaction distance.The quantum fluctuation of side spin is weakest.But for the 1/5-doped antiferromagntic chain,the quantum fluctuation leads to the 47% loss of its staggered susceptibility.

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By density-matrix renormalization group method,the 1/5-doping effect on the spin-1/2 Heisenberg antiferromagnetic chain is investigated.It is shown that adding side spins can weaken the correlations between near-neighbor spins while strengthen those between long-range spins.Because of the broken of sublattice symmetry by side spins,the ferromagnetic and the antiferromagnetic long range orders can coexist in the ground state.Side spins can lower the quantum fluctuations,and the effect will weaken as the increasing of interaction distance.The quantum fluctuation of side spin is weakest.But for the 1/5-doped antiferromagntic chain,the quantum fluctuation leads to the 47% loss of its staggered susceptibility.
For a class of quasi-one-dimensional clusters, by using exact diagonalization, we study the effect of side spins on the spin-spin correlations on chain. Our calculations show that the side spins added in the same sublattice can effectively strengthen the spin-spin correlations in large distance region and make the change tend to flat. It is exactly proved that periodically adding side spins can set up magnetic long-range orders in the ground state. Also we investigate the effect of the density of side spins on correlation strength. The case that two sublattices have different localized spins is discussed.
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.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
We calculate the spin correlation function and the magnetic longitudinal and transverse susceptibilities of a two-dimensional antiferromagnet doped with a small concentration of holes, in the $t\text{\ensuremath{-}}J$ model. We find that the motion of holes generates spin fluctuations that add to the quantum fluctuations, the spin correlations decaying with the inverse of the spin distance, while increasing with doping as the critical hole concentration, where the long-range order disappears, is approached. Moreover, the longitudinal susceptibility becomes finite in the presence of doping due to the strong damping effects induced by the hole motion, while the transverse susceptibility is renormalized by softening effects. Both the longitudinal and transverse susceptibilities increase with doping, the former more significantly than the latter. Our results imply that doping destroys the long-range order while local antiferromagnetic spin correlations persist. This is consistent with experiments on doped copper oxide superconductors.
We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.
By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.