# Topological many-body scar states in dimensions 1, 2, and 3

## TL;DR

This paper introduces an exact method to construct topologically degenerate many-body scar states across 1D, 2D, and 3D systems, exhibiting area law entanglement and properties akin to topological phases.

## Contribution

It provides a novel exact construction of topological many-body scar states in multiple dimensions, linking scar states with topological order.

## Key findings

- Constructed exact topological scar states in 1D, 2D, and 3D.
- Demonstrated these states have area law entanglement.
- Showed these states possess topological degeneracies.

## Abstract

We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These examples of many-body `scar' states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry protected topological phases or topologically ordered phases of matter.