论文标题
投影仪的形式主义，用于保存和丢弃的矩阵产品状态的空间
Projector formalism for kept and discarded spaces of matrix product states
论文作者
论文摘要
任何矩阵产品状态$ |ψ\ rangle $都有一组关联的保存和丢弃的空间，分别用于$ |ψ\ rangle $的描述和更改。这些将系统的整个希尔伯特空间的分区划分为$ |ψ\ rangle $的不可还原$ n $ site变化的相互正交空间。在这里，我们介绍了一个方便的投影仪形式主义和图表符号，以明确表征这些$ n $ site的空间。这极大地促进了明确或隐式采用废弃空间的MPS算法的制定。作为例证，我们为$ n $ site能量差异得出一个明确的表达式，并为具有远距离跳跃的模型进行数值评估。我们还描述了一种用于计算有限MPS基础状态以上低洼$ n $ SITE激发的有效算法。
Any matrix product state $|Ψ\rangle$ has a set of associated kept and discarded spaces, needed for the description of $|Ψ\rangle$, and changes thereof, respectively. These induce a partition of the full Hilbert space of the system into mutually orthogonal spaces of irreducible $n$-site variations of $|Ψ\rangle$. Here, we introduce a convenient projector formalism and diagrammatic notation to characterize these $n$-site spaces explicitly. This greatly facilitates the formulation of MPS algorithms that explicitly or implicitly employ discarded spaces. As an illustration, we derive an explicit expression for the $n$-site energy variance and evaluate it numerically for a model with long-range hopping. We also describe an efficient algorithm for computing low-lying $n$-site excitations above a finite MPS ground state.
