Towers of Quantum Many-body Scars from Integrable Boundary States

TL;DR

This paper constructs models with multiple quantum many-body scars using integrable boundary states, revealing their spectral and entanglement properties, and extending the approach to two-dimensional systems.

Contribution

It introduces a method to generate multiple QMBS from integrable boundary states, linking QMBS to integrable models and demonstrating their low entanglement and periodic dynamics.

Findings

Models exhibit periodic revival dynamics.

QMBS have a restricted spectrum generating algebra.

Entanglement entropy of QMBS follows sub-volume law.

Abstract

We construct several models with multiple quantum many-body scars (QMBS) using integrable boundary states (IBS). Specifically, we focus on the tilted N\'eel states, which are parametrized IBS for the spin-1/2 Heisenberg chain, and show that these states can be used to construct a tower of scar states. Our models exhibit periodic revival dynamics, showcasing a characteristic behavior of superpositions of QMBS. Furthermore, the tower of QMBS found in this study possesses a restricted spectrum generating algebra (RSGA) structure, indicating that QMBS are equally spaced in energy. This approach can be extended to two-dimensional models, which can be decomposed into an array of one-dimensional models. In this case, the tilted N\'eel states again serve as parent states for multiple scar states. These states demonstrate low entanglement entropy, marking them as exact scar states. Notably, their entanglement entropy adheres to the sub-volume law, further solidifying the nonthermal properties of QMBS. Our results provide novel insights into constructing QMBS using IBS, thereby illuminating the connection between QMBS and integrable models.