论文标题
使用螺旋边界条件对二维系统的一维投影
One-dimensional projection of two-dimensional systems using spiral boundary conditions
论文作者
论文摘要
我们将螺旋边界条件（SBC）作为处理有限大小的周期性簇的形状的有用工具。使用SBC，可以将超过两个维度的晶格模型精确地投影到具有转换不变性的一维（1D）周期链上。因此，可以有效地应用于预测的1D模型等现有的1D技术，例如密度 - 矩阵重新归一化组（DMRG），玻孔化，Jordan-Wigner Transformation等。首先，我们描述了实际和动量空间中的二维（2D）正方形和蜂窝晶格紧密结合模型的1D投影方案。接下来，我们讨论状态和基态能量的密度如何接近其热力学极限。最后，为了证明SBC在DMRG模拟中的实用性，我们估计了2D XXZ Heisenberg模型的交错磁化程度，这是XXZ各向异性的函数。
We introduce spiral boundary conditions (SBCs) as a useful tool for handling the shape of finite-size periodic clusters. Using SBCs, a lattice model for more than two dimensions can be exactly projected onto a one-dimensional (1D) periodic chain with translational invariance. Hence, the existing 1D techniques such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., can be effectively applied to the projected 1D model. First, we describe the 1D projection scheme for the two-dimensional (2D) square- and honeycomb-lattice tight-binding models in real and momentum space. Next, we discuss how the density of states and the ground-state energy approach their thermodynamic limits. Finally, to demonstrate the utility of SBCs in DMRG simulations, we estimate the magnitude of staggered magnetization of the 2D XXZ Heisenberg model as a function of XXZ anisotropy.
