Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo

We present a computational framework to identify Hamiltonians of interacting quantum many-body systems that host non-ergodic excited states. We combine quantum Monte Carlo simulations with the recently proposed eigenstate-to-Hamiltonian construction, which maps the ground state of a specified parent Hamiltonian to a single non-ergodic excited state of a new derived Hamiltonian. This engineered Hamiltonian contains non-trivial, systematically-obtained, and emergent features that are responsible for its non-ergodic properties. We demonstrate this approach by applying it to quantum many-body scar states where we discover a previously unreported family of Hamiltonians with spatially oscillating spin exchange couplings that host scar-like properties, including revivals in the quantum dynamics, and towers in the inverse participation ratio; and to many-body localization, where we find a two-dimensional Hamiltonian with correlated disorder that exhibits non-ergodic scaling of the participation entropy and inverse participation ratios of order unity. The method can be applied to other known ground states to discover new quantum many-body systems with non-ergodic excited states.