局部测量与量子链中的纠缠相变
Local measurements and the entanglement transition in quantum spin chains
AI总结：
研究通过局部测量诱导量子链中短程纠缠与长程纠缠的相变，揭示测量后状态的长程相关性及拓扑性质。
摘要：
我们考虑无限量子链中短程纠缠（SRE）与长程有序（因而长程纠缠）状态之间的转变，该转变由局部测量诱导。具体来说，我们假设初始状态处于一个非平凡对称保护拓扑相中，局部对称群为$\mathcal{G} = G \times H$，其中$G$是阿贝尔子群。我们证明，对局部$G$电荷在逐渐增大的区间上的局域测量会将初始SRE状态转化为具有日益增长的长程相关性的状态族。特别是，测量后的状态不能是均匀短程纠缠的。在初始状态由量子细胞自动机从产品态获得的情况下，我们构造了无限体积的测量后状态，并展示了几乎局部的可观测量，这些可观测量是高度相关的。
英文摘要：
We consider the transition between short-range entangled (SRE) and long-range entangled states of infinite quantum spin chains which is induced by local measurements. Specifically, we assume that the initial state is in a non-trivial symmetry-protected topological phase of a compact local symmetry group $\mathcal{G}$. We show that the on-site measurements of an appropriate local charge on intervals of increasing lengths transform the initial SRE state into a family of states with increasingly long-range correlations. In particular, the post-measurement states cannot be uniformly short-range entangled. In the case where the initial state is obtained from a product state using a quantum cellular automaton, we construct the infinite-volume post-measurement state and exhibit almost local observables that are maximally correlated.
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