We demonstrate that nonlinear response functions in many-body systems carry a sharp signature of interactions between gapped low-energy quasiparticles. Such interactions are challenging to deduce from linear response measurements. The signature takes the form of a divergent-in-time contribution to the response—linear in time in the case when quasiparticles propagate ballistically—that is absent for free bosonic excitations. We give a physically transparent semiclassical picture of this singular behavior. While the semiclassical picture applies to a broad class of systems we benchmark it in two simple models: in the Ising chain using a form-factor expansion, and in a nonintegrable model—the spin-1 Affleck-Kennedy-Lieb-Tasaki chain—using time-dependent density matrix renormalization group simulations. We comment on extensions of these results to finite temperatures.

• Received 8 February 2023
• Revised 27 June 2023
• Accepted 15 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.256505

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society