# Quantum Many-body Scars in a Landau Level on a Thin Torus

## TL;DR

This paper explores quantum many-body scars in a Landau level model, revealing exact mappings to constrained spin chains and identifying new scar states with potential implications for quantum Hall systems.

## Contribution

It introduces a mapping of a Landau level model to the PXP model and generalizes it to other fillings, uncovering new quantum many-body scar states.

## Key findings

- Exact mapping to PXP model at filling 1/3
- Identification of scar states with revivals and slow thermalization
- Stability analysis of scars under Hamiltonian perturbations

## Abstract

We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $\nu = 1/3$, the model exactly maps onto the so-called "PXP model", a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $\nu = p/(2p+1)$, and show that the model is equivalent to non-integrable spin-chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.