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arXiv:cond-mat/9807127 · Journal of the Physical Society of Japan

Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu 2O 3 and CaV 2O 5

Shin Miyahara, Matthias Troyer, D. C. Johnston, Kazuo Ueda

Published Nov 1, 1998• 33 citations
arXivHTMLPDF

Abstract

We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu$_2$O$_3$ and CaV$_2$O$_5$ to our results.

DOI
10.1143/jpsj.67.3918

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We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu2_22​O3_33​ and CaV2_22​O5_55​ to our results.
A comprehensive theoretical and experimental study is presented of the magnetic susceptibility versus temperature χ(T) of spin S = 1/2 two- and three-leg Heisenberg ladders and ladder oxide compounds. Extensive quantum Monte Carlo simulations of χ(T) were carried out for both isolated and coupled two-leg ladders with spatially anisotropic intraladder exchange. Accurate fits to these and related literature QMC data were obtained. We have also calculated the one- and two-magnon dispersion relations and the dynamical spin structure factor for anisotropic isolated 2 x 12 ladders. The exchange constants in the two-leg ladder compound SrCu2O3 are estimated from LDA+U calculations. We report the detailed crystal structure of SrCu2O3 and of the three-leg ladder compound Sr2Cu3O5. New experimental χ(T) data are reported for the two-leg ladder cuprates SrCu2O3 and LaCuO_{2.5}, and for the (nominally) two-leg ladder vanadates CaV2O5 and MgV2O5. The new and literature χ(T) data for these compounds and for Sr2Cu3O5 are modeled using our QMC χ(T) simulation fits, and the exchange coupling constants between the spins-1/2 are thereby estimated for each material. The surpisingly strong spatial anisotropy of the bilinear intraladder exchange constants in the cuprate compounds is discussed together with the results of other experiments sensitive to this anisotropy. Recent theoretical predictions are discussed including those which indicate that a four-spin cyclic exchange interaction within a Cu4 plaquette is important to determining the magnetic properties and which can significantly influence the exchange interactions estimated from χ(T) data assuming the presence of only bilinear exchange.
We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV4_44​O9_99​. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.
We present a quantum Monte Carlo study for Heisenberg spin-12\frac{1}{2}21​ two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Znx{}_{x}x​)2{}_{2}2​O3{}_{3}3​, where a large broadening of the 65{}^{65}65Cu NMR lines has been observed in experiment at low temperatures but far above the N\'eel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as x=0.001x=0.001x=0.001 and x=0.0025x=0.0025x=0.0025, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.
We study two planar square lattice Heisenberg models with explicit dimerization or quadrumerization of the couplings in the form of ladder and plaquette arrangements. We investigate the quantum critical points of those models by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\ensuremath{\alpha}={J}^{\ensuremath{'}}/J$. The critical point of the order-disorder quantum phase transition in the ladder model is determined as ${\ensuremath{\alpha}}_{c}=1.9096(2)$ improving on previous studies. For the plaquette model, we obtain ${\ensuremath{\alpha}}_{c}=1.8230(2)$ establishing a first benchmark for this model from quantum Monte Carlo simulations. Based on those values, we give further convincing evidence that the models are in the three-dimensional classical Heisenberg universality class. The results of this contribution shall be useful as references for future investigations on planar Heisenberg models such as concerning the influence of nonmagnetic impurities at the quantum critical point.
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We calculate the uniform and staggered susceptibilities of two-chain spin-12\frac{1}{2}21​ Heisenberg ladders using Monte Carlo simulations. We show that the gap extracted from the uniform susceptibility and the saturation value of the staggered susceptibility are independent of the sign of the interchain coupling ${J}_{\ensuremath{\perp}}$ in the asymptotic limit $|{J}_{\ensuremath{\perp}}|/\stackrel{\ensuremath{\rightarrow}}{J}0.$ Furthermore, we examine the existence of logarithmic corrections to the linear scaling of the gap with $|{J}_{\ensuremath{\perp}}|.$