L: Tang: Infinite-temperature coherent dynamics in scarred models

Abstract: A wide variety of quantum many-body scars can be constructed as condensates of identical quasi- particles atop a simple base state. Within the scar manifold, the quasiparticle operator is often an exact dynamical symmetry, resulting in perfect periodic oscillations of its real-time cor- relation function. Unexpectedly, even though scars constitute a vanishing fraction of the Hilbert space, the correlation function at infinite temperature can continue to exhibit underdamped co- herent oscillations instead of quick relaxation. In this talk, I show that this originates from an approximate dynamical symmetry of the Hamiltonian with respect to the quasiparticle operator in the entire Hilbert space. Furthermore, we show that the quality factor of these oscillations can be quantified by the proximity to this symmetry. In the language of spherical tensors, this corresponds to the effective tensor rank of the perturbation away from an integer energy spectrum.