Title:Hilbert subspace imprint: a new mechanism for non-thermalization

Abstract:The search for non-ergodic mechanisms in quantum many-body systems has become a frontier area of research in non-equilibrium physics. In this Letter, we introduce Hilbert subspace imprint (HSI)-a novel mechanism that enables evasion of thermalization and bridges the gap between quantum many-body scars (QMBS) and Hilbert space fragmentation (HSF). HSI manifests when initial states overlap exclusively with a polynomial scaling (with system size) set of eigenstates. We demonstrate this phenomenon through two distinct approaches: weak symmetry breaking and initial state engineering. In the former case, we observe that ferromagnetic states including those with a single spin-flip display non-thermal behavior under weak U(1) breaking, while antiferromagnetic states thermalize. In contrast, the Z2-symmetric model shows thermalization for both ferromagnetic and antiferromagnetic states. In the latter case, we engineer the initial state prepared by shallow quantum circuits that enhance the overlap with the small target subspace. Our results establish HSI as a mechanism equally fundamental to non-thermalization as QMBS and HSF.