Local measurements and the entanglement transition in quantum spin chains

TL;DR

This paper investigates how local measurements can induce a transition from short-range entangled to long-range correlated states in quantum spin chains, especially those in symmetry-protected topological phases, revealing the emergence of long-range order.

Contribution

It demonstrates how local measurements transform SRE states into states with long-range correlations in symmetry-protected topological phases, providing explicit constructions and analysis.

Findings

Measurements induce long-range correlations in SRE states.

Post-measurement states exhibit non-uniform short-range entanglement.

Constructs explicit infinite-volume states with maximally correlated observables.

Abstract

We consider the transition between short-range entangled (SRE) and long-range ordered (and therefore 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 with local symmetry group $\mathcal{G} = G \times H$, where $G$ is an Abelian subgroup. We show that the on-site measurements of the local $G$-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.