Minimal model for Hilbert space fragmentation with local constraints

Motivated by previous works on a Floquet version of the PXP model [B. Mukherjee et al., Phys. Rev. B 102, 075123 (2020) and B. Mukherjee et al., Phys. Rev. B 101, 245107 (2020)], we study a one-dimensional spin-1/2 lattice model with three-spin interactions in the same constrained Hilbert space (where all configurations with two adjacent S-z = up arrow spins are excluded). We show that this model possesses an extensive fragmentation of the Hilbert space which leads to a breakdown of thermalization upon unitary evolution starting from a large class of simple initial states. Despite the nonintegrable nature of the Hamiltonian, many of its high-energy eigenstates admit a quasiparticle description. A class of these, which we dub as "bubble eigenstates," have integer eigenvalues (including mid-spectrum zero modes) and strictly localized quasiparticles while another class contains mobile quasiparticles leading to a dispersion in momentum space. Other anomalous eigenstates that arise due to a secondary fragmentation mechanism, including those that lead to flat bands in momentum space due to destructive quantum interference, are also discussed. The consequences of adding a (noncommuting) staggered magnetic field and a PXP term, respectively, to this model, where the former preserves the Hilbert space fragmentation while the latter destroys it, are discussed. Making the staggered magnetic field a periodic function of time defines an interacting Floquet system that also evades thermalization and has additional features like exact stroboscopic freezing of an exponentially large number of initial states at special drive frequencies. Finally, we map the model to a U(1) lattice gauge theory coupled to dynamical fermions and discuss the interpretation of some of these anomalous states in this language. A class of gauge-invariant states show reduced mobility of the elementary charged excitations with only certain charge-neutral objects being mobile, suggesting a connection to fractons.