Calculus of continuous matrix product states
Calculus of continuous matrix product states
复制标题
连续矩阵乘积状态的计算
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Verstraete
中科院分区：
文献类型：
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作者：
J. Haegeman;J. Cirac;T. Osborne;F. Verstraete
我们讨论了连续矩阵乘积态的变分类的各种性质，这是最近被引入的一维量子场的一类Anatz态，它是非常成功的一类矩阵乘积态的直接连续极限。我们讨论物理状态的属性，例如，通过详细示出如何计算期望值，以及表示本身固有的属性，例如规范自由度。我们考虑了由多个粒子物种组成的一般平移不变系统，得到了变分参数需要满足的某些正则性。我们还用一节讨论了热力学极限中的平移不变量设置，并展示了连续的矩阵乘积态如何具有本征紫外线截止。最后，我们引入了一个新的状态集，它与原始的连续矩阵乘积态集相切。对于矩阵乘积态的情况，这种结构最近被证明与研究量子自旋链的时间演化和基本激发的新算法的发展有关。从而为一维量子场的类似发展奠定了基础。
We discuss various properties of the variational class of continuous matrix product states, a class of Ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful class of matrix product states. We discuss both attributes of the physical states, e.g., by showing in detail how to compute expectation values, as well as properties intrinsic to the representation itself, such as the gauge freedom. We consider general translation noninvariant systems made of several particle species and derive certain regularity properties that need to be satisfied by the variational parameters. We also devote a section to the translation invariant setting in the thermodynamic limit and show how continuous matrix product states possess an intrinsic ultraviolet cutoff. Finally, we introduce a new set of states, which are tangent to the original set of continuous matrix product states. For the case of matrix product states, this construction has recently proven relevant in the development of new algorithms for studying time evolution and elementary excitations of quantum spin chains. We thus lay the foundation for similar developments for one-dimensional quantum fields.