Stability of the many-body scars in fermionic spin-1/2 models

We study the stability of the many-body scars in spin-1/2 fermionic systems under the most typical perturbations in relevant materials. We find that some families of scars are completely insensitive to certain perturbations. In some other cases they are stable to the first order in perturbation theory. Our analytical results apply to a large class of Hamiltonians that are known [arXiv:2106.10300] to support exact many-body scars. For the numerical calculations we choose the deformed $t-J-U$ model that includes both Heisenberg and Hubbard interactions. We propose two new stability measures that are based on physical observables rather than the fidelity to the exact initial wavefunction. They enable the experimental detection of scars and are more reliable from the theoretical and numerical perspectives. One of these measures may potentially find applications in other systems where the exact many-body scars are equally spaced in energy. In small systems and at small perturbations, a regime particularly relevant for quantum simulators, we identify and describe an additional stability exhibited by the many-body scars. For larger perturbation strengths we observe a distinct mode of ergodicity breaking that is consistent with many-body localization.