Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special nonequilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work, we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent α of spin-spin interactions from the solvable permutationally symmetric limit α=0. First, we numerically establish that, despite the fact that spectral signatures of chaos appear for infinitesimal α, the towers of α=0 energy eigenstates with large collective spin are smoothly deformed as α is increased and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor nonlinearly coupled to an extensive set of bosonic modes. We analytically solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation and show their self-consistent localization in large-spin sectors of the original Hamiltonian for 0<α