Hilbert space fragmentation and exact scars of generalized Fredkin spin chains

Abstract

In this work, based on the Fredkin spin chain, we introduce a family of spin-1/2 many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the one-dimensional Fermi-Hubbard model in the infinite on-site repulsion limit. To demonstrate the many-body scars, we construct an exact middle spectrum eigenstate within each fractured subsector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable nonergodic dynamics by quenching different initial states shown through large-scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays nonergodic dynamics due to sharing the same fragmentation structure and scarring as the Hamiltonian.