Transfer matrices and excitations with matrix product states
Transfer matrices and excitations with matrix product states
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DOI：
10.1088/1367-2630/17/5/053002
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发表时间：
2014-08
影响因子：
3.3
通讯作者：
V. Zauner;D. Draxler;L. Vanderstraeten;M. Degroote;J. Haegeman;M. Rams;V. Stojevic;N. Schuch;F. Verstraete
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文献类型：
--
作者：
V. Zauner;D. Draxler;L. Vanderstraeten;M. Degroote;J. Haegeman;M. Rams;V. Stojevic;N. Schuch;F. Verstraete
利用张量网络态的形式，研究了局域量子多体哈密顿量基态静态关联函数与相应低能激发的色散关系。特别地，我们证明了矩阵乘积状态转移矩阵(MPS-TM)--静态关联函数计算中的中心对象--提供了关于低能色散关系(S)极小值的位置和大小的重要信息，并且我们给出了柱面上一维晶格和连续介质模型以及二维晶格模型的支持性数值数据。我们阐述了MPS-TM本征谱的特殊结构，并对系统低能谱结构与静态关联函数形式之间的密切关系给出了几点论证。最后，我们讨论了在零温下MPS-TM如何连接到模型的精确量子转移矩阵。我们提出了一个重整化群参数来获得MPS的有限键维近似，它允许人们将变分MPS技术(如密度矩阵重整化群)重新解释为沿系统的虚(虚时间)维的Wilson数值重整化群的应用。
We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM’s eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson’s numerical renormalization group along the virtual (imaginary time) dimension of the system.