Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis

Abstract

Here, the authors develop a general formalism to analytically compute the entanglement spectra of exact excited states and use it to obtain the entanglement spectra of the infinite tower of states of the spin-$S$ AKLT models, which are the first analytical examples of what are now called quantum many-body scars. Located in the bulk of the spectrum, these states have a subthermal entanglement entropy, showing for the first time the violation of the strong eigenstate thermalization hypothesis (ETH) in a well-known translation-invariant nonintegrable model.