Engineering many-body quantum Hamiltonians with nonergodic properties using quantum Monte Carlo

We present a computational framework to identify Hamiltonians of interacting quantum many-body systems that host nonergodic 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 nonergodic excited state of a new derived Hamiltonian. This engineered Hamiltonian contains nontrivial, systematically-obtained, and emergent features that are responsible for its nonergodic 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 nonergodic 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 nonergodic excited states.