Chebyshev matrix product state approach for spectral functions
Chebyshev matrix product state approach for spectral functions
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DOI：
10.1103/physrevb.83.195115
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发表时间：
2011-05-10
影响因子：
3.7
通讯作者：
von Delft, Jan
中科院分区：
文献类型：
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作者：
Holzner, Andreas;Weichselbaum, Andreas;von Delft, Jan
我们证明，递归生成的切比雪夫展开式为使用矩阵积态（MPS）方法计算一维晶格模型的零温度谱函数提供了数值有效的表示。这种切比雪夫矩阵乘积状态（CheMPS）方法的主要特点如下：（i）它在谱函数的整个谱宽上实现了统一的分辨率； (ii) 它可以利用后者可以比模型的多体带宽小得多的事实； (iii) 它提供了一个控制良好的展宽方案，可以根据需要解决或消除有限尺寸的效应； (iv) 它基于使用 MPS 工具递归计算一系列切比雪夫向量垂直条 t(n)>，(v) 对于此处分析的所有情况，发现其纠缠熵随着递归阶数 n 的增加而保持有界； (vi)它将随着n的增加而累积的总纠缠熵分布在切比雪夫向量垂直条t(n)>的集合上，其不需要组合成单个向量。通过这种方式，通常限制密度矩阵重整化群（DMRG）方法的纠缠熵的增长被打包成方便管理的单元。我们提出了自旋 1/2 反铁磁海森堡链结构因子的零温 CheMPS 结果，并进行了详细的有限尺寸分析。与三种基准方法进行比较，我们发现 CheMPS (a) 产生的结果在质量上与校正向量 DMRG 相当，但数值成本显着降低； (b) 在有限系统数值预期的限制内，与无限系统的 Bethe ansatz 结果非常一致； (c) 也可以应用于时域，它有可能作为时间相关 DMRG 的可行替代方案（特别是在有限温度下）。最后，我们对非相互作用共振能级模型的情况进行了 CheMPS 的详细误差分析。
We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main features of this Chebyshev matrix product state (CheMPS) approach are as follows: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it can exploit the fact that the latter can be much smaller than the model's many-body bandwidth; (iii) it offers a well-controlled broadening scheme that allows finite-size effects to be either resolved or smeared out, as desired; (iv) it is based on using MPS tools to recursively calculate a succession of Chebyshev vectors vertical bar t(n)>, (v) the entanglement entropies of which were found to remain bounded with increasing recursion order n for all cases analyzed here; and (vi) it distributes the total entanglement entropy that accumulates with increasing n over the set of Chebyshev vectors vertical bar t(n)>, which need not be combined into a single vector. In this way, the growth in entanglement entropy that usually limits density matrix renormalization group (DMRG) approaches is packaged into conveniently manageable units. We present zero-temperature CheMPS results for the structure factor of spin-1/2 antiferromagnetic Heisenberg chains and perform a detailed finite-size analysis. Making comparisons to three benchmark methods, we find that CheMPS (a) yields results comparable in quality to those of correction-vector DMRG, at dramatically reduced numerical cost; (b) agrees well with Bethe ansatz results for an infinite system, within the limitations expected for numerics on finite systems; and (c) can also be applied in the time domain, where it has potential to serve as a viable alternative to time-dependent DMRG (in particular, at finite temperatures). Finally, we present a detailed error analysis of CheMPS for the case of the noninteracting resonant level model.