A remark on matrix product operator algebras, anyons and subfactors
A remark on matrix product operator algebras, anyons and subfactors
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DOI：
10.1007/s11005-020-01254-4
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发表时间：
2019-07
影响因子：
1.2
通讯作者：
Yasuyuki Kawahigashi
中科院分区：
文献类型：
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作者：
Yasuyuki Kawahigashi
我们证明了Bultinck–Mariëna–Williamson–Şahinoğlu–Haegemana–Verstraete最近工作中的数学结构与平坦对称双酉联和子因子论中的筒子代数的结构相同。更具体地说，由具有有限指数和有限深度的子因子产生的平坦对称双酉系满足它们对张量和这种子因子的管状代数的所有要求，并且这种张量的任意子代数在归一化常数上是同构的。此外，对应于可能非平坦对称双酉系的张量所产生的矩阵乘积算子代数与对子因子的平坦对称双酉系所产生的矩阵乘积算子代数同构。
We show that the mathematical structures in a recent work of Bultinck–Mariëna–Williamson–Şahinoğlu–Haegemana–Verstraete are the same as those of flat symmetric bi-unitary connections and the tube algebra in subfactor theory. More specifically, a system of flat symmetric bi-unitary connections arising from a subfactor with finite index and finite depth satisfies all their requirements for tensors and the tube algebra for such a subfactor, and the anyon algebra for such tensors are isomorphic up to the normalization constants. Furthermore, the matrix product operator algebras arising from tensors corresponding to possibly non-flat symmetric bi-unitary connections are isomorphic to those arising from flat symmetric bi-unitary connections for subfactors.