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arXiv · 2205.15775

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

Masahiro Kadosawa·Masaaki Nakamura·Yukinori Ohta·Satoshi Nishimoto
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Abstract

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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Masahiro Kadosawa, Masaaki Nakamura, Yukinori Ohta, Satoshi Nishimoto. 2022-05-31. One-dimensional projection of two-dimensional systems using spiral boundary conditions. https://doi.org/10.1103/physrevb.107.l081104

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