Many-body theory of magnetoelasticity in one dimension

We construct a many-body theory of magnetoelasticity in one dimension and show that the dynamical correlation functions of the quantum magnet, connecting the spins with phonons, involve all energy scales. Accounting for all magnetic states nonperturbatively via the exact diagonalization techniques of Bethe ansatz, we find that the renormalization of the phonon velocity is a nonmonotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons—via hybridization with the continuum of excitations at high energy. We conduct ultrasonic measurements on a high-quality single crystal of the frustrated spin-1/2 Heisenberg antiferromagnet Cs₂CuCl₄ in its nearly one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.