Quantum scars and bulk coherence in a symmetry-protected topological phase

Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence weakly entangled states. At the same time, edge modes certain symmetry-protected topological (SPT) phases can persist away from ground state. In this work we show existence and their implications on bulk such an SPT phase. To end, study eigenstate properties dynamics interacting spin-$1/2$ chain with three-site ``cluster'' terms hosting ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ Focusing regime, find that eigenstates volume-law entanglement coexist area-law throughout spectrum. We subset latter be constructed by virtue repeated cluster excitations even or odd sublattice chain, resulting equidistant ``tower'' states, analogous to phenomenology scars. further demonstrate these scarred support nonthermal expectation values local operators exhibit signatures order at finite energy densities. Studying out-of-equilibrium states drawn noninteracting ``cluster basis,'' unveil nonthermalizing observed long timescales if clusters sites are energetically detuned. case, remain essentially confined one two sublattices inhomogeneous configurations cannot equilibrate thermalization full system is impeded. Our sheds light role preserving temperature possibility coherent models beyond long-lived modes.