We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-1 Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains $\left(J^{\prime }\ll J\right)$ and the isotropic triangular lattice $\left(J^{\prime }=J\right)$. We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at ${(J^{\prime }/J)}_c\sim 0.42$, signaled by the sudden closing of the spin gap. Coming from the magnetically ordered side, the computation of the spin stiffness within Schwinger boson theory predicts the instability of the spiral magnetic order toward a magnetically disordered phase with one-dimensional features at ${(J^{\prime }/J)}_c\sim 0.43$. The agreement of these complementary methods, along with the strong difference found between the intra- and the interchain DMRG short spin-spin correlations for sufficiently large values of the interchain coupling, suggests that the interplay between the quantum fluctuations and the dimensional crossover effects gives rise to the one-dimensionalization phenomenon in this frustrated spin-1 Hamiltonian.

中文翻译：

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各向异性三角晶格上spin-1海森堡模型的一维化

我们研究了反铁磁自旋1 Heisenberg模型基态上尺寸交叉对各向异性三角晶格的影响，该各向异性三角晶格插在弱耦合的Haldane链体系之间 $（{Ĵ}^{\prime }\ll Ĵ）$ 和各向同性的三角形晶格 $（{Ĵ}^{\prime }=Ĵ）$。我们使用密度矩阵重归一化组（DMRG）和Schwinger玻色子理论，该理论在高于鞍点解的高斯校正水平上进行。我们的DMRG结果表明，解耦的自旋链与螺旋形有序状态之间突然过渡${（{Ĵ}^{\prime }/Ĵ）}_C〜0.42$，是自旋间隙突然关闭的信号。从磁有序的角度出发，施温格玻色子理论中自旋刚度的计算预测了螺旋磁阶对具有一维特征的磁无序相的不稳定性。${（{Ĵ}^{\prime }/Ĵ）}_C〜0.43$。这些互补方法的一致性，以及对于链间耦合足够大的值，在链内和链间DMRG短自旋相关之间发现的强差异，表明量子涨落和尺寸交叉效应之间的相互作用产生了这个沮丧的自旋1哈密顿量的一维化现象。