Abstract:
 
Ever since its experimental observation, quantum many-body scarring as a weaker form of ergodicity breaking and ETH violation than the previously known integrability and many-body localization, has generated intensive theoretical efforts in searching exact excited states of models known to be non-integrable. Most of the examples found so far, fall in to the unified framework of spectrum generating algebra, sharing common features such as equal-distant energy spacing and area-law of entanglement entropy. In this talk, I present two distinct models, in one and two dimensions, with novel paradigms of allowing exact eigenstates or integrable subspectra. Their energy gaps and entanglement entropies of are also studies rigorously to show that neither fall into the categorial of conventional quantum many-body scars (QMBSs). These two models were constructed with two opposite approaches: the first model starts with a frustration-free bulk Hamiltonian and introduce boundary terms to split the ground state degeneracy. The second adds perturbation to an integrable Hamiltonian that violates Yang-Baxter equation in general, but leaves it satisfied only in certain subspaces of the Hilbert space, where the Bethe Ansatz eigenstates survive. These complementing strategies should help provide insight into the zoo of known QMBSs and formulating a general theory to guide their search in the future.