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, 5–6. 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.