Onsager's scars in disordered spin chains

The Eigenstate Thermalization Hypothesis (ETH) is a plausible scenario of the thermalization of isolated quantum systems. Although there is no rigorous proof, it is widely believed to hold for a large class of non-integrable systems. However, recent experiments with Rydberg atoms [1] observed robust periodic revivals from certain initial states, implying anomalously slow thermalization, even though the system is non-integrable. This athermal phenomenon called quantum many-body scars (QMBS) results from the existence of ETH-violating eigenstates [2].

We propose a new class of spin models with QMBS [3] by making full use of the so-called Onsager algebra. Focusing on a certain Onsager-algebra element, we can explicitly write down a one-parameter family of scar states as an MPS with a finite bond dimension. Remarkably, we do not impose translational invariance on our model. To our knowledge, this is the first explicit example of disordered QMBS models. Moreover, our model is easy to generalize to one with an arbitrary spin quantum number and multi-parameter scar states.

[1] H. Bernien et al., Nature 551, 579 (2017).
[2] C. J. Turner et al., Nat. Phys. 14, 745 (2018).
[3] N. Shibata, N. Yoshioka, and H. Katsura, Phys. Rev. Lett. 124, 180604 (2020).