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.
We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.
We propose the strongly tilted Bose-Hubbard model as a natural platform to explore Hilbert-space fragmentation (HSF) and fracton dynamics in two dimensions in a setup and regime readily accessible in optical lattice experiments. Using a perturbative ansatz, we find HSF when the model is tuned to the resonant limit of on-site interaction and tilted potential. First, we investigate the quench dynamics of this system and observe numerically that the relaxation dynamics strongly depends on the chosen initial state-one of the key signatures of HSF. Second, we identify fractonic excitations with restricted mobility leading to anomalous transport properties. Specifically, we find excitations that show one-dimensional diffusion (z=1/2) as well as excitations that show subdiffusive behavior in two dimensions (z=3/4). Using a cellular automaton, we analyze their dynamics and compare it to an effective hydrodynamic description.
The occurrence of prethermal Hilbert space fragmentation (HSF) in periodically driven quantum systems has its roots in the emergence of additional, approximate, kinetic constraints at special driving frequencies. Here, the authors show that the out-of-time-ordered correlators (OTOCs) of a driven fermion chain with open boundary condition exhibit a signature of such HSF. At the special drive frequencies where such prethermal HSF occurs, the OTOCs display periodic unscrambling of information, which provides a yet unexplored, experimentally testable, marker for prethermal fragmentation.
Suppressing Floquet thermalization is an important goal in the field of Floquet engineering. Here, we propose a driving transparency mechanism to suppress the Floquet thermalization in periodically driven tilted lattices of interacting spinless fermions. By leveraging the interplay between the tilting and interaction, the system can be engineered to prevent direct energy absorption from the driving at particular frequencies. We analytically determine these driving transparency frequencies through the Floquet time-dependent perturbation theory. The system is near-integrable at the driving transparency frequencies. The suppression of thermalization by the driving transparency is demonstrated numerically by the violation of the Floquet eigenstate thermalization hypothesis, the retention of the initial state, and the logarithmic growth of entanglement entropy. Our work provides an intuitive way to suppress Floquet thermalization and offers an opportunity to engineer exotic nonequilibrium Floquet states in tilted lattice systems.
We study a periodically driven spin-
1/2 Ising chain with a nearest-neighbour coupling and longitudinal field while a weak transverse field induces single-spin flips. Through Floquet perturbation theory (FPT), we obtain signatures of Hilbert space fragmentation (HSF) and an unconventional form of dynamical localisation which we call the Floquet freezing. Our analysis suggests that these observations emerge due to a single Floquet selection rule that dictates the prethermal dynamics. For a special value of the field-to-interaction strength ratio together with commensurate drive periods, this rule permits only a constrained subset of bulk spin flips, leading to prethermal HSF in the full spin-
1/2 Hilbert space. Under open boundary conditions, the same rule suppresses boundary spin flips up to higher order in perturbation and produces long-lived prethermal edge memory, which is neither topological in origin nor is a strong zero mode. Furthermore, under periodic boundary conditions, the largest surviving fragment is exactly the PXP sector at leading order and therefore exhibits Floquet-inherited scar phenomenology in the prethermal window. At higher commensurate ratios of field strength to interaction strength, all first-order single-spin-flip channels are suppressed and the system enters a regime of Floquet freezing. Hence, our study leverages the selection rules obtained through Floquet perturbation theory to obtain exotic prethermal phenomena at different parameter regimes.
We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude
Q0 and frequency
ωD. The Hamiltonian of the spin chain hosts a thermodynamically large number of
Z2-valued conserved quantities
Wℓ on the links
ℓ. This allows us to study the Floquet dynamics of this chain within a given sector with fixed values of
Wℓ. For the sector with all
Wℓ=1, we find signatures of quantum many-body scar states for
ℏωD≫Q0; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering
ωD, we find an ergodic regime exhibiting fast thermalization consistent with the prediction of the (Floquet) eigenstate thermalization hypothesis. In addition, we identify special drive frequencies
ωn∗=Q0/(2nℏ) (where
n=1,2,3,⋯) at which the Floquet Hamiltonian exhibits prethermal strong Hilbert space fragmentation (HSF) with the largest fragment being ergodic; in contrast, a weak HSF is found at
ωn′=Q0/[ℏ(2n+1)] (where
n=0,1,2,⋯). We also study the sector with
Wℓ={⋯1,1,−1,1,1,−1⋯} which shows strong HSF at
ωn∗ but no fragmentation at
ωn′. Our analysis indicates that the strong HSF in this sector harbors an integrable largest fragment. We provide numerical support for our analytical and perturbative results using exact-diagonalization (ED) studies on finite chains of length
L≤24. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.