Multi-magnon quantum many-body scars from tensor operators

Quantum many-body scars are eigenstates at finite energy density which violate the eigenstate thermalization hypothesis. If scars form towers that are equally spaced in energy, any initial state that has high overlap with the scars exhibit persistent coherent oscillations in quench experiments. Such towers can be generated by repeated action of ladder operators (which may be interpreted as quasiparticle operators) on a low-entanglement base state. In this talk, I will discuss a systematic derivation of scarred Hamiltonians based on irreducible tensor operators, which constitute a natural operator basis for Hamiltonians satisfying a spectrum-generating algebra (SGA) in the scarred manifold. The basis allows us to embed low-entanglement multi-magnon states as exact eigenstates in an otherwise thermalizing Hamiltonian. Each magnon carries a fixed energy and quasi-momentum that is either equal to zero or a fixed, finite value. While the discussion focuses on spin-1/2 chains, the framework can be applied for any spin, spatial dimension, or continuous non-Abelian symmetry that generates the scarred subspace.