Local measurements and the entanglement transition in quantum spin chains

Abstract: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.

v1 --> v2. Major generalization. The result applies to an arbitrary compact group. Additional minor changes

arXiv:2602.05914 [math-ph]

(or arXiv:2602.05914v3 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2602.05914 Focus to learn more arXiv-issued DOI via DataCite

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