Observation of conformal field theory spectra in a quantum simulator
Abstract
Conformal field theories (CFTs) feature prominently in high-energy physics1,2, statistical mechanics3 and condensed matter4–6. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions4,7, including their entanglement, correlations and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions—recovering universal energy ratios characteristic of the underlying field theories8,9. Specifically, we develop and implement a modulation technique to resolve the finite-size spectra of a Rydberg chain, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also use local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By using a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator but also provides a technique for diagnosing a priori unknown universality classes in future experiments. Measurements on an array of optically trapped neutral atoms at a quantum phase transition provide a direct observation of the universal excitation spectrum predicted by conformal field theory.
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BibTeX
@article{sun2026observation,
title = {{Observation of conformal field theory spectra in a quantum simulator}},
author = {Xiangkai Sun and Yuan Le and Stephen Naus and Richard Bing-Shiun Tsai and Lewis R.B Picard and Sara Murciano and Michael Knap and Jason Alicea and Manuel Endres},
journal = {Nature},
year = {2026},
month = sep,
doi = {10.1038/s41586-026-10904-x},
url = {https://hal.science/hal-05744840v1},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Observation of conformal field theory spectra in a quantum simulator
AU - Xiangkai Sun
AU - Yuan Le
AU - Stephen Naus
AU - Richard Bing-Shiun Tsai
AU - Lewis R.B Picard
AU - Sara Murciano
AU - Michael Knap
AU - Jason Alicea
AU - Manuel Endres
PY - 2026
DA - 2026/09/10
JO - Nature
DO - 10.1038/s41586-026-10904-x
UR - https://hal.science/hal-05744840v1
AB - Conformal field theories (CFTs) feature prominently in high-energy physics1,2, statistical mechanics3 and condensed matter4–6. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions4,7, including their entanglement, correlations and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions—recovering universal energy ratios characteristic of the underlying field theories8,9. Specifically, we develop and implement a modulation technique to resolve the finite-size spectra of a Rydberg chain, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also use local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By using a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator but also provides a technique for diagnosing a priori unknown universality classes in future experiments. Measurements on an array of optically trapped neutral atoms at a quantum phase transition provide a direct observation of the universal excitation spectrum predicted by conformal field theory.
SN - 0028-0836
SN - 1476-4687
ER -