Boundary transitions from a single round of measurements on gapless quantum states
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915490723528704 |
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| author | Liu, Yue Murciano, Sara Mross, David F. Alicea, Jason |
| author_facet | Liu, Yue Murciano, Sara Mross, David F. Alicea, Jason |
| contents | 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 non-trivial 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 wavefunction, 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 non-trivial 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary transitions from a single round of measurements on gapless quantum states Liu, Yue Murciano, Sara Mross, David F. Alicea, Jason Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory 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 non-trivial 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 wavefunction, 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 non-trivial 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. |
| title | Boundary transitions from a single round of measurements on gapless quantum states |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.07830 |