Quantum acoustics: the coherent state formalism for electron-lattice interaction*

The electron-lattice interplay is a linchpin in numerous solid-state phenomena. However, lattice vibrations have been (almost) exclusively considered within the phonon and number state framework, neglecting their dual description emphasizing the wave aspect. To address this limitation, we have developed the coherent state picture of lattice vibrations, following the development of quantum optics. This formalism offers an intuitive and powerful methodology for understanding the interaction between electrons and the lattice in real space. In particular, by means of quantum-acoustical theory, we have been able to treat the electron-lattice interaction nonperturbatively and coherently. While our results align with those obtained through perturbation theory in the weak-coupling regime, we find that nonperturbative coherence effects can be the key to some of the most puzzling enigmas in condensed matter, such as the mysteries of universal Planckian resistivity and temperature-dependent Drude peak shift in strange metals.