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Monte Carlo simulation with tensor network states

机译:张量网络状态的蒙特卡洛模拟

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We demonstrate that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with a large virtual bond dimension. We use the simple update rule introduced by H. C. Jiang et al. [Phys. Rev. Lett 101, 090603 (2008)] to obtain the tensors describing the ground state wave function of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of linear sizes up to L = 16 and virtual bond dimensions up to D = 16. The finite size magnetization errors are 0.003(2) and 0.013(2) at D = 16 for a system of size L = 8,16, respectively. Finite D extrapolation provides exact finite size magnetization for L = 8, and reduces the magnetization error to 0.005(3) for L = 16, significantly improving the previous state-of-the-art results.
机译:我们证明了蒙特卡洛采样可以用来有效地提取具有较大虚拟键维的投影纠缠对状态的期望值。我们使用H. C. Jiang等人介绍的简单更新规则。 [物理Rev. Lett 101,090603(2008)],获得张量来描述反铁磁海森堡模型的基态波函数,并评估线性尺寸最大为L = 16且周期边界条件为方格的有限尺寸能量和交错磁化强度虚拟键的尺寸最大为D =16。对于大小为L = 8,16的系统,在D = 16时,有限大小的磁化误差分别为0.003(2)和0.013(2)。有限的D外推法可为L = 8提供精确的有限尺寸磁化强度,并且对于L = 16可将磁化误差减小至0.005(3),从而大大改善了先前的最新技术成果。

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