连续矩阵乘积态的广义分析
Generalised ansatz for continuous Matrix Product States
摘要：
最近的研究表明，连续矩阵乘积状态（cMPS）不能表示任何矩阵乘积状态（MPS）的连续极限状态，根据后者的某种自然定义。缺少的元素是MPS的传递矩阵中的投影仪。在这里，我们提供了一个广义的分析cMPS，是能够表达的连续极限的任何MPS。它由具有不同边界条件的cMPS之和组成，每个cMPS都连接到一个辅助状态。这个新的映射可以被解释为在cMPS集合的闭包处的状态与标准cMPS的级联。前者可以看作是热力学极限下的cMPS，或具有无界范数的矩阵。我们提供了几个例子，并讨论了结果。
英文摘要：
Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural definition of the latter. The missing element is a projector in the transfer matrix of the MPS. Here we provide a generalised ansatz of cMPS that is capable of expressing the continuum limit of any MPS. It consists of a sum of cMPS with different boundary conditions, each attached to an ancilla state. This new ansatz can be interpreted as the concatenation of a state which is at the closure of the set of cMPS together with a standard cMPS. The former can be seen as a cMPS in the thermodynamic limit, or with matrices of unbounded norm. We provide several examples and discuss the result.
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