Quantum scars as embeddings of weakly broken Lie algebra representations
Kieran Bull, Jean-Yves Desaules, Zlatko Papić
Abstract
Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium. An example of such nonthermalizing behavior is the phenomenon of quantum many-body scars, which has been experimentally observed in Rydberg-atom quantum simulators. Here, the authors show that many-body scars can generally be viewed as forming approximate subspaces of ``broken'' Lie algebra representations. Furthermore, they use an iterative process to identify perturbations which ``correct'' the broken Lie algebra, resulting in improved quantum revivals from special initial states. The description of embedded Lie algebra representations unifies several theoretical models, which feature exact many-body scars, with experimentally realized models, such as the constrained Rydberg-atom system, where scars only form an approximate Lie algebra representation.