Onsager's Scars in Disordered Spin Chains

TL;DR

This paper introduces disordered quantum spin chain models with quantum many-body scars, constructed using Onsager symmetry, which exhibit non-thermalizing behavior and violate the eigenstate thermalization hypothesis.

Contribution

It presents the first explicit disordered quantum many-body scarred model using Onsager symmetry for arbitrary spin quantum number S.

Findings

Scar states have area-law entanglement and are representable as matrix product states.

Scar states are trapped in periodic orbits and do not thermalize.

The model is the first explicit example of disordered quantum many-body scars.

Abstract

We propose a class of non-integrable quantum spin chain models that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct such scarred models for arbitrary spin quantum number $ S $. There are two types of scar states, namely, coherent states associated to an Onsager-algebra element and one-magnon scar states. While both of them are highly-excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred model.