Quantum many-body scars (QMBS) represent a mechanism for weak ergodicity breaking, characterized by the coexistence of atypical nonthermal eigenstates within an otherwise thermalizing many-body spectrum. In this work, we revisit the spin-1 $XY$ model on a periodic chain and construct several new families of exact scar eigenstates embedded within its extensively degenerate manifolds that owe their origins to an interplay of $\mathrm{U}\left(1\right)$ magnetization conservation and chiral symmetries. We go beyond previously studied towers of states and first identify a novel set of interference-protected eigenstates resembling Fock space cage states, where destructive interference confines the wave function to sparse subgraphs of the Fock space. These states exhibit subextensive entanglement entropy, and when subjected to a transverse magnetic field, form equally spaced states whose coherent superpositions display long-lived fidelity oscillations. We further reveal a simpler organizing principle behind these nonthermal states by utilizing the commutant algebra framework, specifically by demonstrating that they are simultaneous eigenstates of noncommuting local operators. Moreover, in doing so, we uncover two more novel families of exact scars: a tower of volume-entangled states, and a set of mirror-dimer states with some free local degrees of freedom. Our results illustrate the power and interplay of interference-based and algebraic mechanisms of nonergodicity, offering systematic routes to identifying and classifying QMBS in generic many-body quantum systems.

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• Eigenstate thermalization
• Quantum quench
• Quantum scars
• Exact solutions for many-body systems
• Quantum spin chains