Multimagnon quantum many-body scars from tensor operators
Long-Hin Tang, Nicholas O’Dea, Anushya Chandran
Abstract
We construct a family of three-body spin-$\frac{1}{2}$ Hamiltonians with a superextensive set of infinitely long-lived multimagnon states. A magnon in each such state carries either quasimomentum zero or fixed ${p}_{0}\ensuremath{\ne}0$, and energy $\mathrm{\ensuremath{\Omega}}$. These multimagnon states provide an archetypal example of quantum many-body scars: they are eigenstates at finite-energy density that violate the eigenstate thermalization hypothesis, and lead to persistent oscillations in local observables in certain quench experiments. On the technical side, we demonstrate the systematic derivation of scarred Hamiltonians that satisfy a restricted spectrum-generating algebra using an operator basis built out of irreducible tensor operators. This operator basis can be constructed for any spin, spatial dimension, or continuous non-Abelian symmetry that generates the scarred subspace.