Perturbation Theory for Parent Hamiltonians of Matrix Product States
Perturbation Theory for Parent Hamiltonians of Matrix Product States
复制标题
矩阵积态母哈密顿量的微扰理论
DOI：
10.1007/s10955-015-1204-2
复制
发表时间：
2014
影响因子：
1.6
通讯作者：
M. Wolf
中科院分区：
文献类型：
--
作者：
O. Szehr;M. Wolf
本文研究了矩阵乘积态的正则父哈密顿量的基态子空间对局部扰动的稳定性。我们证明了这样的哈密顿量的谱隙在弱的局部扰动下保持稳定，即使在热力学极限下，整个扰动可能没有界。我们的讨论是基于以前的工作Yarotsky开发了一个相对有界的经典哈密顿量子微扰的微扰理论。我们利用重整化过程，在大尺度上将矩阵乘积态的父哈密顿量转化为经典哈密顿量加上一些微扰。因此，我们可以扩展Yarotsky的结果以提供矩阵乘积状态的父哈密顿量的微扰理论，并恢复独立贡献的一些发现（Cirac等人，Phys Rev B 8（11）：115108，2013）和（Michalakis和Pytel，Comm Math Phys 322（2）：277-302，2013）。
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky’s results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277–302, 2013).