Hilbert subspace imprint: a new mechanism for non-thermalization

The search for non-ergodic mechanisms in quantum many-body systems has become a frontier area of research in non-equilibrium physics. In this work, we introduce Hilbert subspace imprint (HSI)—a new mechanism that enables evasion of thermalization, standing as an independent non-ergodic mechanism alongside 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.