One-dimensional projection of two-dimensional systems using spiral boundary conditions
One-dimensional projection of two-dimensional systems using spiral boundary conditions
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DOI：
10.1103/physrevb.107.l081104
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发表时间：
2022-05
影响因子：
3.7
通讯作者：
Masahiro Kadosawa;M. Nakamura;Y. Ohta;S. Nishimoto
中科院分区：
文献类型：
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作者：
Masahiro Kadosawa;M. Nakamura;Y. Ohta;S. Nishimoto
我们引入螺旋边界条件（sbc）作为处理有限尺寸周期星团形状的有用工具。利用sbc，二维以上的晶格模型可以精确地投影到一维周期链上，具有平移不变性。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一维模型。首先，我们描述了二维（2D）方形晶格和蜂窝晶格紧密结合模型在实空间和动量空间中的一维投影格式。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sbc在DMRG模拟中的实用性，我们估计了2D XXZ海森堡模型的交错磁化强度作为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.