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arXiv:cond-mat/9908044 · International Journal of Modern Physics B

HEISENBERG INTEGER SPIN CHAINS IN A UNIFORM MAGNETIC FIELD

Lorenzo Campos Venuti, Elisa Ercolessi, G. Morandi, P. Pieri, M. Roncaglia

Published Apr 10, 2002• 10 citations
arXivHTMLPDF

Abstract

We investigate both numerically and analytically the behavior of a spin-1 antiferromagnetic isotropic Heisenberg chain in an external uniform magnetic field. Extensive DMRG studies of chains up to N = 80 sites extend previous analyses and obtain the zero-temperature correlation functions. We argue that, despite the presence of a magnetic field, the model is still well described by an O(3) nonlinear σ-model. A saddle-point analysis, that also includes Gaussian fluctuations, is developed for the latter both at zero and finite temperatures. Its predictions are compared with those of the numerical analysis and with the existing experimental literature.

DOI
10.1142/s0217979202010099

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We investigate both numerically and analytically the behavior of a spin-1 antiferromagnetic isotropic Heisenberg chain in an external uniform magnetic field. Extensive DMRG studies of chains up to N = 80 sites extend previous analyses and obtain the zero-temperature correlation functions. We argue that, despite the presence of a magnetic field, the model is still well described by an O(3) nonlinear σ-model. A saddle-point analysis, that also includes Gaussian fluctuations, is developed for the latter both at zero and finite temperatures. Its predictions are compared with those of the numerical analysis and with the existing experimental literature.
We present here a nonlinear sigma-model (NLσM) study of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. We find, already at the mean-field level, excellent agreement with recent and very accurate Density Matrix Renormalization Group (DMRG) studies, and that up to the highest values of the field for which a comparison is possible, for the staggered magnetization and the transverse spin gap. Qualitative but not quantitative agreement is found between the NLσM predictions for the longitudinal spin gap and the DMRG results. The origin of the discrepancies is traced and discussed. Our results allow for extensions to higher-spin chains that have not yet been studied numerically, and the predictions for a spin-2 chain are presented and discussed. Comparison is also made with previous theoretical approaches.
We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S=1/2,1,3/2S=1/2,1,3/2S=1/2,1,3/2 spins when a weak magnetic field is applied on a few sites, using White's density-matrix renormalization-group method. For the S=1S=1S=1 chain there exists only one length scale in the system which determines the behavior of the one- and two-point correlation functions both around the local perturbation and near the free boundary. For the critical half-odd-integer spin cases the exponent of the spin-spin correlation function was found to be $\ensuremath{\eta}=1$ and the exponent of the decay of the site magnetization around the perturbed site is ${x}_{m}=\ensuremath{\eta}/2.$ Close to a free boundary, however, the behavior is completely different for S=1/2S=1/2S=1/2 and S>1/2.S>1/2.S>1/2.
Magnetic-field tuning of equal-time longitudinal and transverse correlations is investigated for the antiferromagnetic isotropic spin-1/2 Heisenberg chain. Full exact diagonalization of a ten-site periodic ring is used at kBT/J=0.15 over 0≤h/J≤2.6, where h=gμBB. The field breaks spin-rotational symmetry, increases uniform magnetization, redistributes longitudinal and transverse correlation weight, and drives the system toward the fully polarized state above the saturation field hs=2J. Below saturation, longitudinal correlations acquire a uniform m² background and field-dependent oscillatory structure, whereas transverse antiferromagnetic correlations weaken as the density of reversed spins decreases. The finite-temperature magnetization rounds the zero-temperature level crossings and saturation threshold. The numerical results are interpreted using the Tomonaga-Luttinger-liquid description and checked against exact limiting values. The analysis provides a reproducible finite-chain account of field-controlled spin correlations and identifies the distinctions required when connecting static calculations to scattering experiments.
The response of an open spin chain with isotropic antiferromagnetic interactions to a uniform magnetic field is studied by classical Monte Carlo simulations. It is observed how the induced on-site magnetization is nonuniform, due to the occurrence of edge staggered terms which decay exponentially over a distance equal to the zero-field correlation length of the infinite chain. The total magnetic moment associated to each staggered term is found to be about half of the original single-spin magnitude and to decrease as the inverse of temperature (i.e., to behave as a Curie-like moment). The numerical results are compared to recent NMR findings in spinless-doped Y2BaNiO5;{\mathrm{Y}}_{2}{\mathrm{BaNiO}}_{5};Y2​BaNiO5​; the remarkable agreement found shows that, for temperatures above the Haldane gap, the classical approach gives a correct picture of the boundary effects observed in the Heisenberg S=1S=1S=1 chain.
We present in this paper a nonlinear \ensuremath{\sigma}-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a calculation at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a steadily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of the art as well as with previous analytical approaches is also made.
In this work we study the Heisenberg XXZ antiferromagnetic model for spin S and dimension d in the presence of an external longitudinal magnetic field. First, we essay a variational approach which uses as trial function a version of the analytic expression for the ground state given by the paired nonmagnetic excitation (PNME) theory [M. Lagos and G. G. Cabrera, Solid State Commun. 67, 221 (1988); Phys. Rev. B 38, 659 (1988)], generalized in order to incorporate the external field. The ground-state energy, sublattice magnetization, and magnetic susceptibility are obtained. Subsequently, we solve the problem numerically for a chain of 12 spins (S=1 and S=3/2) using the Lancz\"os method [E. Dagotto and A. Moreo, Phys. Rev. D 31, 865 (1985)]. The two approaches give excellent concordance over a wide range of the parameters of the model. We show that our analytic trial function represents accurately the ground state of the system for anisotropies ranging from the Ising limit to the almost isotropic Heisenberg model for all values of the field. Moreover, it accounts for the several antiferromagnetic and ferromagnetic phases occurring for different values of the magnetic field with the same precision. The critical fields of the transitions are predicted correctly. Also, results for various spin values S in two and three dimensions are presented.