Entanglement of excited states after measurements in conformal field theory
Abstract
We study the entanglement of low-energy excited states after a fixed-outcome projective measurement on a spatial interval in a (1+1)-dimensional conformal field theory (CFT). We restrict to post-selected measurement outcomes whose induced boundary condition flows in the infrared to a conformal boundary condition. Such an outcome is represented by a slit carrying that boundary condition, while excited states are introduced by operator insertions in the Euclidean path integral. After mapping the replicated slit geometry to a disk, the excited-state contribution to the post-measurement Rényi entropy is expressed as a normalized boundary-CFT correlation function. We apply this framework to the compact free boson CFT. For the chiral current excitation, the relevant ratios are given by current hafnians. We also study coherent superpositions of J and J̅, and of conjugate compact vertex operators. In the conjugate-vertex case, the ordinary-cylinder second Rényi ratio is independent of the relative phase, whereas the finite-slit post-measurement ratio contains phase-sensitive interference terms. Finally, we describe free-fermion and multi-Slater determinant methods for testing these predictions in the critical XX chain.
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BibTeX
@misc{chen2026entanglement,
title = {{Entanglement of excited states after measurements in conformal field theory}},
author = {Hui-Huang Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04268},
eprint = {2607.04268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entanglement of excited states after measurements in conformal field theory
AU - Hui-Huang Chen
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2607.04268
UR - https://arxiv.org/abs/2607.04268
AB - We study the entanglement of low-energy excited states after a fixed-outcome projective measurement on a spatial interval in a (1+1)-dimensional conformal field theory (CFT). We restrict to post-selected measurement outcomes whose induced boundary condition flows in the infrared to a conformal boundary condition. Such an outcome is represented by a slit carrying that boundary condition, while excited states are introduced by operator insertions in the Euclidean path integral. After mapping the replicated slit geometry to a disk, the excited-state contribution to the post-measurement Rényi entropy is expressed as a normalized boundary-CFT correlation function. We apply this framework to the compact free boson CFT. For the chiral current excitation, the relevant ratios are given by current hafnians. We also study coherent superpositions of J and J̅, and of conjugate compact vertex operators. In the conjugate-vertex case, the ordinary-cylinder second Rényi ratio is independent of the relative phase, whereas the finite-slit post-measurement ratio contains phase-sensitive interference terms. Finally, we describe free-fermion and multi-Slater determinant methods for testing these predictions in the critical XX chain.
ER -