周期边界条件的有效矩阵乘积状态法
Efficient Matrix Product State Method for periodic boundary conditions
摘要：
介绍了一种计算一维周期边界晶格模型基态的有效方法。该方法适用于矩阵乘积态（MPS）的表示，与密度矩阵重整化群（DMRG）方法相关。它改进了Verstraete等人以前的方法。我们引入了MPS矩阵长积的因子分解过程，将计算量从m^5减少到m^3，其中m是矩阵维数，在典型情况下m ~ 100 - 1000。我们测试的方法上的S=1/2和S=1海森堡链。它也适用于非线性不变的情况。新方法使得周期性边界条件下的基态计算与传统的开放边界系统的DMRG计算一样有效。
英文摘要：
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable to non-translationally invariant cases. The new method makes ground state calculations with periodic boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
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