Floquet engineering of Hilbert space fragmentation in Stark lattices

The concept of Hilbert space fragmentation (HSF) has recently been put forward as a routine to break quantum ergodicity. Although HSF exists widely in models with dynamical constraints, it is still challenging to tune it. Here, we propose a scheme to tune the HSF in a one-dimensional tilted lattice of interacting spinless fermions with periodically driven tunneling. For weak tunneling strength, the dynamics for a long range of time is governed by effective Hamiltonians with kinetic constraints, which appear as density-dependent tunneling. Through a Floquet time-dependent perturbation theory, we analytically derive two different resonance frequencies, at which some particular tunneling processes are resonant. At the nonresonance frequencies, the system is strongly constrained and exhibits a strong HSF. At the two different resonance frequencies, the kinetic constraints are partly released and the system exhibits another two different strong HSFs. We can tune the HSF by changing the driving frequency. We support the perturbation analysis with exact numerical simulation of the entanglement entropy, the density correlation functions, and the saturated local density profiles. Our result provides a promising way to control HSF through Floquet engineering.