Many-body theory of magneto-elasticity in one dimension

TL;DR

This paper develops a comprehensive many-body theory of magneto-elasticity in one-dimensional quantum magnets, revealing complex phonon behaviors and validating predictions through ultrasonic experiments on a frustrated spin chain.

Contribution

It introduces a non-perturbative theoretical framework for magneto-elasticity in 1D, combining Bethe ansatz with experimental validation, highlighting phonon renormalization and hybridisation mechanisms.

Findings

Phonon velocity renormalizes non-monotonically with magnetic field.

Identification of a new phonon attenuation mechanism via hybridisation.

Experimental confirmation of theoretical predictions using ultrasonic measurements.

Abstract

We construct a many-body theory of magneto-elasticity 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 non-perturbatively via the exact diagonalisation techniques of Bethe ansatz, we find that the renormalisation of the phonon velocity is a non-monotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons - via hybridisation 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 $\textrm{Cs}_{2}\textrm{CuCl}_{4}$ in its one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.