Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $\theta$ angle of $\pi$. Introducing rhombic SIA shifts this angle from $\pi$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $\theta$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators.