Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models
Daniel K. Mark, Cheng-Ju Lin, Olexei I. Motrunich
Abstract
Exact ``towers'' of quantum many-body scar states are recently discovered sets of states in some many-body nonintegrable systems. They are evenly spaced in energy and do not obey the eigenstate thermalization hypothesis. Here, the authors provide a unified framework of proving several towers of states known in the literature. This sheds light on the general structure of exact scar towers, and on the specific models themselves: the 1D AKLT models, spin-1 XY model, and a spin-\textonehalf{} domain wall conserving model. In particular, they provide a simple proof for the scars in the AKLT models and discover a ``pyramid'' of exact states in the spin-\textonehalf{} model.
Topics & Concepts
Hamiltonian (control theory)Operator (biology)Integrable systemTheoretical physicsSimple (philosophy)PhysicsEigenvalues and eigenvectorsDiagonalMathematicsMathematical physicsQuantum mechanicsGeometryBiochemistryGenePhilosophyChemistryTranscription factorRepressorMathematical optimizationEpistemologyQuantum many-body systemsQuantum and electron transport phenomenaPhysics of Superconductivity and Magnetism