Quantum many-body scars" (QMBS) is currently one of the most active research topics in many-body physics. QMBS are atypical eigenstates of non-integrable Hamiltonians that weakly violate ergodicity. Initiated by the pioneering experiment in Rydberg quantum simulator [1], the field has seen rapid growth over the last 6 years [2]. I will first briefly review the relevant portion of this literature, highlighting our contribution to it. After this, I will discuss the construction of exact QMBS at infinite temperature in the non-integrable staggered Heisenberg model [3].  While the Bethe ansatz can be used to construct exact states in the low-magnon sectors in spite of the non-integrability [4], its extension to higher magnon sectors is notoriously difficult. I will then present a complimentary approach to construct exact QMBS in the high-magnon sectors by taking a symmetric superposition of triplet coverings [5]. The number of such symmetric tensor scars scales quadratically with system size, and their entanglement is highly tunable, which ranges from volume to logarithmic to area law depending on the choice of basis for the triplets. I will discuss the two-parameter state-diagram in the Bell basis, which involves volume - log law transition. Finally, I will conclude by showing some examples in the conventional basis of triplets.
 References:
1) Probing many-body dynamics on a 51-atom quantum simulator, Bernien et al, Nature 551, 579-584 (2017).
2) Weak ergodicity breaking from quantum many-body scars, Turner et al, Nature Physics 14 (7), 745-749 (2018).
3) Stable infinite-temperature eigenstates in SU (2)-symmetric nonintegrable models, Turner et al, arXiv:2407.11956.
4) Exact generalized Bethe eigenstates of the non-integrable alternating Heisenberg chain, Melendrez et al, arXiv:2501.14017.
5) Symmetric tensor scars with tunable entanglement from volume to area law, Mukherjee et al, arXiv:2501.14024v2.