Phase diagram and post-quench dynamics in a double spin-chain system in transverse fields

We propose and explore the physics of a toy multiferroic model by coupling two distinct dipolar XXZ models in transverse fields. We determine first the rich ground-state phase diagram of the model using density matrix renormalization group techniques. Then, we explore the dynamics of the system after global and local quenches, using the time-evolving block decimation algorithm. After a global quench, the system displays decaying coupled oscillations of the electric and magnetic spins, in agreement with the Eigenstate Thermalization Hypothesis (ETH) for many-body interacting quantum systems. Notably, the spin-spin interactions lead to a sizeable quadratic shift in the oscillation frequency as the inter-chain coupling is increased. Local quenches lead to a light-cone-like propagation of excitations. In this case, the inter-chain coupling drives a transfer of energy between the chains that generates a novel fast spin-wave mode along the 'magnetic' chain at the speed of the 'electric' spin-wave. This suggests a limited control mechanism for faster information transfer in magnetic spin chains using electric fields that harnesses the electric dipoles as intermediaries.