Boundary transitions from a single round of measurements on gapless quantum states

Abstract

Measurements can qualitatively alter correlations and entanglement emerging in gapless quantum matter. We show how a single round of measurements on gapless quantum systems can, upon rotating the measurement basis, induce nontrivial transitions separating regimes displaying universal characteristics governed by distinct boundary conformal field theories. We develop the theory of such "measurement-induced boundary transitions" by investigating a gapless parent of the one-dimensional cluster state, obtained by appropriately symmetrizing a commuting projector Hamiltonian for the latter. Projective measurements on the cluster state are known to convert the wave function, after post-selection or decoding, into a long-range-ordered Greenberger-Horne-Zeilinger (GHZ) state. Similar measurements applied to the gapless parent (i) generate long-range order coexisting with power-law correlations when post-selecting for uniform outcomes, and (ii) yield power-law correlations distinct from those in the pre-measurement state upon decoding. In the post-selection scenario, rotating the measurement basis preserves long-range order up until a critical tilt angle marking a measurement-induced boundary transition to a power-law-ordered regime. Such a transition—which does not exist in the descendant cluster state—establishes new connections between measurement effects on many-body states and nontrivial renormalization-group flows. We extend our analysis to tricritical Ising and three-state Potts critical theories, which also display measurement-induced boundary transitions, and propose general criteria for their existence in other settings.

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