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Low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets

机译：二维稀释的海森堡量子反铁磁体的低能激发

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We study the low-energy dynamics of S= 1/2 antiferromagnetic Heisenberg clusters constructed by diluting a square lattice at vacancy concentration p at and below the percolation threshold p~* ≈ 0.407. The finite-size scaling behavior of the average excitation gap, (Δ)～L~(-z), where L is the cluster length, is obtained using quantum Monte Carlo results for an upper bound Δ~* to Δ, derived from sum rules. At the percolation threshold, we obtain a dynamic exponent z = 3.6±0.1 ≈2D_f for clusters with singlet (5 = 0) ground state. Here D_f = 91/48 is the fractal dimensionality of the percolating cluster. We argue that this large dynamic exponent-roughly twice that expected for quantum-rotor excitations-is a consequence of weakly interacting localized effective magnetic moments, which form due to local sublattice imbalance. This picture is supported by an extremal-value analysis of local spectral gaps, which delivers an exponent relation (between z and two exponents characterizing the local-gap distribution) reproduced by our simulation data. However, the average (Δ~*) over all clusters, which have mostly ground-state spin S>0, scales with a smaller exponent than for the 5 = 0 clusters alone; z≈1.5D_f. Lanczos exact diagonalization for small clusters show that typically, S→S-1 in the lowest-energy excitations while the dominant spectral weight originates from S→S+1 excitations. Thus, the scaling of (Δ~*) for clusters with ground state 5>0 does not reflect the lowest-energy excitations but the higher S→S+ 1 excitations. This result can be understood within a valence bond picture. To further explore the scenario of localized moments, we introduce a classical dimer-monomer aggregation model to study the distribution of nearest-neighbor sites forming dinners (which are the objects used in mapping to the quantum-rotor model) and unpaired spins (monomers). The monomers are localized and, thus, effective magnetic moments should form in the spin system. We also study the lowest triplet excitation of S=0 clusters using quantum Monte Carlo calculations in the valence bond basis. The triplet is concentrated at some of the classical monomer regions, confirming the mechanism of moment formation. The number of spins (and moment regions) affected by the excitation scales as a nontrivial power of the cluster size. For a dimer-diluted bilayer Heisenberg model with weak interlayer coupling (where the system remains Neel ordered), there is no sublattice imbalance. In this case we find z≈D_f, consistent with quantum-rotor excitations. For a single layer at p~* we find z≈2 = D, which indicates that the weakly interacting localized moment mechanism is valid only exactly at the percolation point. There is a crossover behavior close to the percolation point.
机译：我们研究了通过在空位浓度p处和低于渗流阈值p〜*≈0.407时稀释正方形晶格而构造的S = 1/2反铁磁Heisenberg簇的低能动力学。使用总和得出的上界Δ〜*的量子蒙特卡罗结果，获得平均激发间隙的有限尺寸缩放行为（Δ）〜L〜（-z），其中L为簇长。规则。在渗透阈值处，对于具有单重态（5 = 0）基态的簇，我们获得了动态指数z = 3.6±0.1≈2D_f。 D_f = 91/48是渗流团簇的分形维数。我们认为，这种大的动态指数-大约是量子转子激发所预期的两倍-是由于局部亚晶格失衡而形成的局部有效磁矩相互作用弱的结果。该图片由局部光谱间隙的极值分析提供支持，该分析提供了模拟数据所再现的指数关系（z与两个表征局部间隙分布的指数之间）。但是，所有基团的基态自旋S> 0的平均值（Δ**）的标度比单独5 = 0的聚簇更小。 z≈1.5D_f。 Lanczos对小星团的精确对角化显示，通常，最低能量激发中的S→S-1，而主要频谱权重则来自S→S + 1激发。因此，对于基态5> 0的簇，（Δ〜*）的标度不能反映出最低的能量激发，而可以反映出较高的S→S + 1激发。在价键图片中可以理解该结果。为了进一步探索局域矩的情况，我们引入了经典的二聚体-单体聚集模型，以研究形成晚餐（映射到量子转子模型中使用的对象）和不成对自旋（单体）的最近邻居位点的分布。 。单体是局部的，因此，应该在自旋系统中形成有效的磁矩。我们还以价键为基础，使用量子蒙特卡洛计算研究了S = 0簇的最低三重态激发。三重态集中在一些经典的单体区域，证实了力矩形成的机理。受激发影响的自旋数（和力矩区域）作为簇大小的非平凡幂而定。对于具有弱层间耦合（系统保持Neel有序）的二聚体稀释的Heisenberg模型，不存在亚晶格失衡。在这种情况下，我们发现z≈D_f，与量子转子激励一致。对于p 〜*的单层，我们发现z≈2= D，这表明弱相互作用的局部矩机制仅在渗流点才有效。在渗透点附近有一个交叉行为。

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