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Journal of Jiangsu University of Science and Technology

Numerical Research on Quasi-one-dimensional Heisenberg Antiferromagnetic Spin System

Dongfang Chen

Published Jan 1, 2005• 0 citations
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Abstract

The magnetic order of a special quasi-one-dimensional Heisenberg antiferromagnetic spin model with numerical density matrix renormalization groups is discussed. The ground energy per unit cell, spin correlation function and the spin gap are calculated. Results show that the quasi-one-dimensional spin system has magnetic long-rang order under ground state and the spin correlation on chain is short-rang.

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The magnetic order of a special quasi-one-dimensional Heisenberg antiferromagnetic spin model with numerical density matrix renormalization groups is discussed. The ground energy per unit cell, spin correlation function and the spin gap are calculated. Results show that the quasi-one-dimensional spin system has magnetic long-rang order under ground state and the spin correlation on chain is short-rang.
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.
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.
We present results of a numerical renormalization-group study of the isotropic S=1 Heisenberg chain. The density-matrix renormalization-group techniques used allow us to calculate a variety of properties of the chain with unprecedented accuracy. The ground-state energy per site of the infinite chain is found to be e0{\mathit{e}}_{0}e0​\ensuremath{\simeq}-1.401 484 038 971(4). Open-ended S=1 chains have effective S=1/2 spins on each end, with exponential decay of the local spin moment away from the ends, with decay length \ensuremath{\xi}\ensuremath{\simeq}6.03(1). The spin-spin correlation function also decays exponentially, and although the correlation length cannot be measured as accurately as the open-end decay length, it appears that the two lengths are identical. The string correlation function shows long-range order, with g(\ensuremath{\infty})\ensuremath{\simeq}-0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=\ensuremath{\pi}, is the Haldane gap, which we find to be \ensuremath{\Delta}\ensuremath{\simeq}0.410 50(2). We find many low-lying excited states, including one- and two-magnon states, for several different chain lengths. The magnons have spin S=1, so the two-magnon states are singlets (S=0), triplets (S=1), and quintuplets (S=2). For magnons with momenta near \ensuremath{\pi}, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.
The ground state energy, the correlation functions and the excitation energy of a Heisenberg antiferromagnetic chain of spin S are investigated by the real-space renormalization-group method. The asymptotic form ( S →∞) of the ground state energy is compared with the result obtained by the spin wave theory. The calculated correlation function < S ( i ) · S ( i + l ) > shows no long range order for a system of finite S . The excitation spectrum is found to have singular dips at q =(odd integer) ×π/3 n a . This is associated with the shortcoming of the three-site renormalization.
The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as u a with a > 2 where u denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives even in the presence of randomness. The string order behaves as u 2β with β∼0.37 in agreement with the recent prediction of real space renormalization group theory (β=(3−5)/2≃0.382\beta =(3-\sqrt{5})/2 \simeq 0.382β=(3−5​)/2≃0.382). The physical picture of this behavior in this model is also discussed.