One-dimensional projection of two-dimensional systems using spiral boundary conditions

Article

关键词: HEISENBERG;    ANTIFERROMAGNET;    XXZ;   

DOI  :  10.1103/PhysRevB.107.L081104

来源: SCIE

【 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 effec-tively 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.

【 授权许可】

Free