相互作用 Majorana 链中的纠缠与 von Neumann 代数的转变
Entanglement in interacting Majorana chains and transitions of von Neumann algebras
AI总结：
研究可精确求解的相互作用 Majorana 链，揭示四格点模型中由跃迁控制的纠缠熵跃变及 von Neumann 代数类型转变。
摘要：
我们考虑具有两格点相互作用的 Majorana 晶格，这种相互作用由费米子双线性型的一般函数构成。在格点上费米子数目很大的极限下，这些模型可精确求解。四格点链展现出由跃迁参数控制的量子相变，并表现为通过约束单侧模 Hamiltonian 得到的不连续纠缠熵。受 AdS/CFT 对应中近期工作的启发，我们在整个相图中识别出 von Neumann 算子代数类型之间的转变。我们发现形式为 II$_1\leftrightarrow$ III $\leftrightarrow$ I$_\infty$ 的转变；在强相互作用极限下，这些转变简化为 II$_1\leftrightarrow$ I$_\infty$，并在那里连接非因子化与因子化基态。我们的结果在一个可控多体模型中提供了此类转变的新颖实现。
英文摘要：
We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II$_1\leftrightarrow\,$III$\,\,\leftrightarrow\,\,$I$_\infty$ that reduce to II$_1\leftrightarrow\,\,$I$_\infty$ in the strongly interacting limit, where they connect non-factorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.
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