彭罗斯镶嵌上的自旋波和局域磁化
Spin waves and local magnetizations on the Penrose tiling
摘要：
我们考虑彭罗斯镶嵌上的海森堡反铁磁体，一个具有非均匀Neel序基态的准周期系统。在线性自旋波近似下研究了自旋波的能量和波函数。在低能量下发现线性色散规律，与其他二分反铁磁体一样，其有效自旋波速度低于正方形晶格。本征模的空间特性以几种不同的方式表征。在低能量下，本征态相对扩展，并显示多重分形标度。在较高的能量下，状态更加局部化，并且根据能量的不同，限制在指定配位数的位点上。计算了这种反铁磁体的基态能量和局部交错磁化强度。Percular空间投影，以显示这种“复杂的”基态的基本简单性。一个简单的分析模型，两层海森堡星，提出来解释交错的磁化分布在这个反铁磁系统。
英文摘要：
We consider a Heisenberg antiferromagnet on the Penrose tiling, a quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions are studied in the linear spin wave approximation. A linear dispersion law is found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes are characterized in several different ways. At low energies, eigenstates are relatively extended, and show multifractal scaling. At higher energies, states are more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations are calculated. Perpendicular space projections are presented in order to show the underlying simplicity of this "complex" ground state. A simple analytical model, the two-tier Heisenberg star, is presented to explain the staggered magnetization distribution in this antiferromagnetic system.
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