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Magnetic responses of randomly depleted spin ladders

机译：随机耗尽的自旋梯的磁响应

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The magnetic responses of a spin-1/2 ladder doped with nonmagnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by Sigrist and Furusaki [M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)] and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte Carlo simulations gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response that is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature and with quantum Monte Carlo simulations at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu_2PO_6 compound and other spin-gapped materials are briefly mentioned.
机译：结合分析和数值方法研究了掺有非磁性杂质的自旋1/2阶梯的磁响应。考虑了挫败感导致不可通约性的制度。 Sigrist和Furusaki对开创性工作的结果进行了一些改进[M. Sigrist和A. Furusaki，物理学报。 Soc。日本。 65，2385（1996）]，还分析了由于相互作用导致的布里渊磁化曲线的偏差。我们首先讨论键合算子平均场理论中单个杂质周围的磁分布以及杂质之间的有效相互作用。将结果与密度矩阵重归一化组计算进行比较。特别是，这些数量表明对过渡到不相称政权敏感。然后，我们通过有效的居里常数集中于零场磁化率的行为。在零温度下，我们对普通二分晶格上Sigrist和Furusaki的结果进行了掺杂相关的校正，并由于链断裂效应而精确计算了梯形簇的分布。用精确的对角线化和量子蒙特卡洛模拟求解有效模型可得出居里常数的温度依赖性。在随机二聚体模型中可以理解其高温极限，而低温尾部则与实空间重归一化组场景兼容。有趣的是，求解完整的微观模型不会显示出与各向同性阶梯中的杂质饱和相对应的平稳状态。分析的第二个磁响应是磁曲线。在自旋间隙量级的场以下，磁化过程由相互作用的杂质自旋的物理学控制。随机二聚体模型显示出捕获了大部分曲线，这说明了由于相互作用导致与布里渊行为的偏差。有效的模型计算与零温度下的密度矩阵重归一化组计算和有限温度下的量子蒙特卡洛模拟非常吻合。总而言之，不可通量性对磁化率和磁曲线都没有表现出很强的定性作用。简要提到了BiCu_2PO_6化合物和其他自旋能隙材料的实验结果。

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