We present several different calculations pertaining to the nature of the low-energy excitations of the site-diluted S=1/2 Heisenberg antiferromagnet, in particular at the percolation point. We present a picture of excitations originating from an effective low-energy subsystem consisting of localized magnetic moments. At the percolation point, these moments lead to an anomalously large dynamic exponent; z=3.6(1). The magnetic moments are shown to originate from local sublattice imbalance, which we study quantitatively using a classical dimer-monomer model. The localization properties of triplet excitations of clusters with singlet ground state are examined using simulations in the valence bond basis. The triplet is shown to affect predominantly sites on the classical monomer regions. The number of sites affected grows as a non-trivial power of the cluster size. We also study a bilayer model, where there is no sublattice imbalance. Accordingly, we find a much smaller dynamic exponent, consistent with quantum rotor (or possibly fracton) excitations.
Comment on ``Quantum Phase Transition of the Randomly Diluted Heisenberg Antiferromagnet on a Square Lattice''
In Phys. Rev. Lett. 84，4204（2000）（cond-mat/9905379）中，Kato等人提出了量子Monte Carlo结果，表明二维反铁磁海森堡模型中随机非磁性位点的临界浓度等于经典逾渗密度; pc=0.407254。这些数据还表明，一个令人惊讶的依赖性的临界指数的自旋S的磁性网站，与一个渐进的方法，以经典的渗流指数S走向无穷大。我在这里认为，指数实际上是S-独立的，等于那些经典渗流。Kato等人发现的明显的S依赖行为是由于模拟中的温度效应以及掩盖小晶格真实渐近标度行为的量子效应。
Schwinger boson mean field perspective on emergent spins in diluted Heisenberg antiferromagnets
利用非均匀系统的Schwinger玻色子平均场论（SBMFT），我们研究了正方形和Bethe晶格上低能自旋激发在其渗流阈值的性质。最佳的SBMFT参数被解释为现场电位和配对振幅，这使得能够解释为什么在这个系统中出现的局部时刻发展稀释[L。Wang和A. W. Sandvik，Phys. Rev. 97，117204（2006）; H. J. Changlani等人，ibid 111，157201（2013）]以及为什么相应的单粒子频率被驱动到非常低的值。我们将讨论如何我们的平均场计算表明，存在的亚晶格不平衡和长程反铁磁秩序之间的强有力的联系，以及为什么线性自旋波理论是不足以捕捉这种关系。在SBMFT框架内，我们还提取了一个能量尺度的紧急时刻之间的相互作用，这表明定性协议与多体计算。
An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.
Bose glass behavior in (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ representing the randomly diluted quantum spin-1/2 chains
格位稀释化合物（Yb $_{1-x}$ Lu $_x$）$_4$ As $_3$是线性海森堡反铁磁体有限段的一种罕见的实现，是研究一维反铁磁体中淬火无序场依赖效应的理想模型化合物。它区别于迄今为止研究的系统在两个方面-在纯样品中的随机性和能隙的性质。我们测量了（Yb $_{1-x}$ Lu $_x$）$_4$ As $_3$单晶在19.5T磁场下的比热。确定了在垂直于链的外加磁场中由磁性子系统产生的贡献$C_{\perp}$。与纯Yb $_4$作为$_3$相比，其中$C_{\perp}$表示间隙开口，对于稀释的系统，在低温下发现非指数衰减，这与玻色玻璃相建立的比热的热力学标度一致。
We investigate the zero- and finite-temperature properties of the bond-random $s=1/2$ Heisenberg antiferromagnet on the pyrochlore lattice by the exact diagonalization and the Hams--de Raedt methods. We find that the randomness induces the gapless quantum spin liquid (QSL) state, the random-singlet state. Implications to recent experiments on the mixed-anion pyrochlore-lattice antiferromagnet Lu$_2$Mo$_2$O$_5$N$_2$ exhibiting gapless QSL behaviors are discussed.
Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
We investigate the impact of site dilution by setting the on-site repulsion strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach first to recover the zero dilution (undiluted $x=1$) properties, including $U$ dependence of insulator to metal crossover temperature scale $T^*$ and long-range staggered antiferromagnetic ordering temperature ($T_N$). For the non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of $T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unc…
This short note documents some of the pyrochlore magnetization plateaus resulting from the arguments of Pal & Lal that were not mentioned in arxiv:1902.06475v1. These are (layered) "Kagome"-like plateaus that are commensurate with the pyrochlore lattice, including an exact wavefunction for the $\frac{m}{m_s} = \frac{5}{6}$ plateau state.
