Integrability, Thermalization, and Quantum Scars in a Constrained Hamiltonian

We study the quantum dynamics of a simple translation invariant, center-of-mass preserving model of interacting fermions in one dimension, which arises in multiple experimentally realizable contexts. We show that this model exhibits a Hilbert space that fractures into exponentially many dynamically disconnected Krylov subspaces. Each of the exponentially large Krylov subspaces can either be integrable or non-integrable. We analytically find examples of several integrable subspaces, and show evidence for the validity of Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable subspace. This model thus exhibits phenomenology associated with quantum scars, i.e. the fate of an initial product state under time-evolution depends on the properties of the Krylov subspaces it has weights in. In addition, some of the non-integrable Krylov subspaces show conventional quantum scars, which manifest as revivals and slow thermalization of certain charge density wave configurations.