Projector matrix product operators, anyons and higher relative commutants of subfactors
Projector matrix product operators, anyons and higher relative commutants of subfactors
复制标题
投影矩阵乘积算子、任意子和子因子的更高相对交换子
DOI：
10.1007/s00208-022-02519-0
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Yasuyuki Kawahigashi
中科院分区：
文献类型：
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作者：
Yasuyuki Kawahigashi
琼斯的子因子理论中的双酉连接产生了一个有限深度的子因子，给出了一个4-张量，它出现在Bultinck-Mariën-Williamson-Haegeman-Verstraete最近关于二维拓扑序和任意子的工作中。在他们的工作中，他们有一个特殊的投影称为投影矩阵乘积算子。我们证明了这个长度投影的范围自然地与双幺正联络所产生的子因子的第k个较高的相对交换子相同。这给出了二维拓扑序和子因子理论之间的进一步联系。
A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck–Mariën–Williamson–Şahinoğlu-Haegeman–Verstraete on two-dimensional topological order and anyons. In their work, they have a special projection called a projector matrix product operator. We prove that the range of this projection of lengthkis naturally identified with thekth higher relative commutant of the subfactor arising from the bi-unitary connection. This gives a further connection between two-dimensional topological order and subfactor theory.