用螺旋边界条件作二维系统的一维投影
One-dimensional projection of two-dimensional systems using spiral boundary conditions
摘要：
我们引入螺旋边界条件（SBCs）作为一个有用的工具，用于处理有限大小的周期性集群的形状。使用SBC，可以将二维以上的晶格模型精确地投影到具有平移不变性的一维（1D）周期链上。因此，现有的一维技术，如密度矩阵重整化群（DMRG）、玻色化、Jordan-Wigner变换等，可以有效地应用于投影的1D模型。首先，我们描述了二维正方形和蜂窝格子紧束缚模型在实空间和动量空间的一维投影方案。接下来，我们讨论态密度和基态能量如何接近它们的热力学极限。最后，为了证明SBCs在DMRG模拟中的实用性，我们估计了作为XXZ各向异性的函数的2D XXZ海森堡模型的交错磁化强度的大小。
英文摘要：
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.
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