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 systemsunder the most typical perturbations in relevant materials. We find that somefamilies of scars are completely insensitive to certain perturbations. In someother cases they are stable to the first order in perturbation theory. Ouranalytical results apply to a large class of Hamiltonians that are known[arXiv:2106.10300] to support exact many-body scars. For the numericalcalculations we choose the deformed $t-J-U$ model that includes both Heisenbergand Hubbard interactions. We propose two new stability measures that are basedon physical observables rather than the fidelity to the exact initialwavefunction. They enable the experimental detection of scars and are morereliable from the theoretical and numerical perspectives. One of these measuresmay potentially find applications in other systems where the exact many-bodyscars are equally spaced in energy. In small systems and at smallperturbations, a regime particularly relevant for quantum simulators, weidentify and describe an additional stability exhibited by the many-body scars.For larger perturbation strengths we observe a distinct mode of ergodicitybreaking that is consistent with many-body localization.