非均匀AKLT模型的块自旋密度矩阵
Block Spin Density Matrix of the Inhomogeneous AKLT Model
摘要：
研究了一维AKLT自旋链模型的非齐次推广。每个晶格点的自旋可能不同。在一定条件下，该AKLT模型的基态是唯一的，并由价键固体（VBS）状态描述。我们计算了在这种基态中连续块体自旋的密度矩阵。密度矩阵与块体外部的自旋无关。它是对角化的，并被证明是一个投影到一个子空间。我们证明了对于大块，密度矩阵在子空间中表现为恒等式。冯诺伊曼熵与Renyi熵一致，并等于饱和值。
英文摘要：
We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.
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