量子细胞自动机与物质的可逆相
Quantum cellular automata and invertible phases of matter
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中文总结 AI 辅助
该研究在一致局部有限度量空间上引入费米子和玻色子可逆准局域代数，证明其布饶尔等价类群与可逆态相群、量子细胞自动机稳定等价类群同构，还构造了ℤ²上的非平凡可逆态与量子细胞自动机。
中文摘要 AI 辅助
我们在具有无限维局域冯·诺依曼代数的一致局部有限度量空间X上引入并研究（费米子和玻色子）可逆准局域代数。我们证明这类代数的布饶尔等价类群同构于可逆态的相群，以及X×ℤ上量子细胞自动机的稳定等价类群。利用可逆准局域代数的对称幺半范畴的K-理论和有界扩散同构，我们提出了Kitaev所猜想的可逆相的Ω-谱的定义。随后我们证明c=1/2手征马约拉纳费米子网和(E₈)₁共形网提供了布饶尔非平凡的可逆准局域代数，从而在ℤ²上给出了非平凡可逆态和量子细胞自动机的显式构造。此外，我们证明有理对角共形场论的时间切片网具有晶格自由度，这意味着任何全纯共形网的离散化是可逆的。
英文摘要
We introduce and study (fermionic and bosonic) invertible quasi-local algebras over uniformly locally finite metric spaces $X$ with infinite-dimensional local von Neumann algebras. We show that the group of Brauer equivalence classes of such algebras is isomorphic to both the group of phases of invertible states and the group of stable equivalence classes of quantum cellular automata over $X\times \mathbb{Z}$. Using K-theory of the symmetric monoidal category of invertible quasi-local algebras and bounded spread isomorphisms, we propose a definition of an $Ω$-spectrum of invertible phases as conjectured by Kitaev. We then show that the $c=\frac{1}{2}$ chiral Majorana fermion net and the $(E_{8})_{1}$ conformal net provide Brauer non-trivial invertible quasi-local algebras, thus providing explicit constructions of non-trivial invertible states and quantum cellular automata on $\mathbb{Z}^{2}$. In addition, we show that the time-slice nets of rational diagonal conformal field theories admit lattice degrees of freedom, which implies the discretization of any holomorphic conformal net is invertible.
