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In this work, based on the Fredkin spin chain, we introduce a family ofspin-$1/2$ many-body Hamiltonians with a three-site interaction featuring afragmented Hilbert space with coexisting quantum many-body scars. Thefragmentation results from an emergent kinetic constraint resembling theconserved spin configuration in the 1D Fermi-Hubbard model in the infiniteonsite repulsion limit. To demonstrate the many-body scars, we construct anexact eigenstate that is in the middle of the spectrum within each fracturedsub-sector displaying either logarithmic or area-law entanglement entropy. Theinterplay between fragmentation and scarring leads to rich tunable non-ergodicdynamics by quenching different initial states that is shown through largescale matrix product state simulations. In addition, we provide a Floquetquantum circuit that displays non-ergodic dynamics as a result of sharing thesame fragmentation structure and scarring as the Hamiltonian.

Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains