Many Body Scars as a Group Invariant Sector of Hilbert Space

We present a class of Hamiltonians H for which a sector of the Hilbert space invariant under a Lie group G, which is not a symmetry of H, possesses the essential properties of many-body scar states. These include the absence of thermalization and the non-decaying “revivals” of special initial states in time evolution. Some of the scar states found in earlier work may be viewed as special cases of our construction. A particular class of examples concerns interacting spin-1/2 fermions on a lattice consisting of N sites (Fermi-Hubbard model as a special case), and we show that it contains two families of N+1 scar states. One of these families, which was found in recent literature, is comprised of the well-known eta-pairing states that have been linked to superconductivity. We find another family of scar states which is U(N) invariant. Both families and most of the group-invariant scar states produced by our construction in general, give rise to the off-diagonal long range order which survives at high temperatures and is insensitive to the details of the dynamics. Such states could be used for reliable quantum information processing because the information is stored non-locally, and thus cannot be easily erased by local perturbations. This talk will be based on arXiv:2007.00845.