Strongly-tilted field induced Hamiltonian dimerization and nested quantum scars in the 1D spinless Fermi-Hubbard model

We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective Hamiltonian, and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization, which are composed of two distinct sets of constrained nearest-neighbor hopping terms: one set acting exclusively on odd bonds and the other on even bonds. Specifically it is shown that each part can be independently mapped onto the well-known PXP model, therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model. As a consequence, we numerically demonstrate this system can host the so-called quantum many-body scars, which present dynamical revivals and ergodicity-breaking behaviors. However in sharp contrast with traditional quantum many-body scars, here the scarring states in our model driven by different parts of Hamiltonian will revive in different periods, and those of double parts can display a biperiodic revival pattern, both originating from the Hamiltonian dimerization. Besides, the condition of off-resonance is also discussed and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics. Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.