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.
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 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.
Periodically driven closed quantum systems are expected to eventually heat up to infinite temperature; reaching a steady state described by a circular orthogonal ensemble. However, such finite driven systems may exhibit sufficiently long prethermal regimes; their properties in these regimes are qualitatively different from that of their corresponding infinite temperature steady states. These, often experimentally relevant, prethermal regimes host a wide range of phenomena; they may exhibit dynamical localization and freezing, host Floquet scars, display signatures of Hilbert space fragmentation, and exhibit time crystalline phases. Such phenomena are often accompanied by emergent approximate dynamical symmetries which have no analogue in equilibrium systems. In this review, we provide a pedagogical introduction to the origin and nature of these symmetries and discuss their role in shaping the prethermal phases of a class of periodically driven closed quantum systems.
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.
Hilbert space fragmentation (HSF) is a mechanism for generating quantum many-body scar (QMBS), which provides a route to weakly break ergodicity. Many scarred systems possess an exponentially large number of zero-energy states due to the chiral symmetry induced bipartition of the Hilbert space. In this work, we study the QMBS phenomenology under the interplay between the chiral symmetry and pseudo HSF, where the Hilbert space is approximately fragmented into different blocks. We consider a model of tilted chain of interacting spinless fermions with periodically varying tunneling strength. At small tunneling strength, we analytically derive the resonance conditions under which the system is described by an effective model with chiral symmetry and pseudo HSF. We find that the interplay between the two gives rise to a highly localized zero-energy QMBS when the particle number is even. This zero-energy QMBS induces an unusual scarred dynamical phenomenon. Specifically, the fidelity from a simple initial state oscillates around a finite fixed value without decaying, instead of showing the typical decaying collapse and revival observed when the particle number is odd and in common scarred systems. We show that the signature of the unusual scarred dynamical behaviour can also be detected in the original driven system by measuring local observables. Our findings enrich the scar phenomenon and deepen the understanding of the relation between Hilbert space structure and QMBS.
We investigate the onset and mechanism of Hilbert space fragmentation (HSF) in a chain of strongly interacting Rydberg atoms subject to local dephasing. It is found that the emergence of multiple long-lived metastable states is fundamentally tied to HSF of the driven-dephasing Rydberg atom system. We demonstrate that the manifesting HSF is captured by a dephasing PXP model that supports multiple degenerate zero modes. These modes form disconnected, block-diagonal subspaces of maximally mixed states, which consist of many-body spin states sharing the same symmetry. A key result is the identification of the underlying symmetry in the HSF, where conserved quantities in each subspace are defined by the consecutive double excitation addressing operator. Moreover, we show explicitly that the number of the fragmented Hilbert space grows exponentially with the chain length, following a modified Fibonacci sequence. Our work provides insights into many-body dynamics under dynamical constraints and opens avenues for controlling and manipulating HSF in Rydberg atom systems.