# Hilbert space fragmentation in a long-range system

## TL;DR

This paper investigates how the interaction range affects Hilbert space fragmentation and scar states in a generalized Fredkin spin chain, revealing their robustness and impact on out-of-equilibrium dynamics.

## Contribution

It demonstrates that scar states and weak Hilbert space fragmentation persist across various interaction ranges in a Fredkin spin chain model.

## Key findings

- Scar states survive for almost any interaction range.
- Hilbert space fragmentation remains weak across different ranges.
- Out-of-equilibrium dynamics show persistent oscillations or stationary magnetization profiles.

## Abstract

We study the role of the interaction range on the Hilbert space fragmentation and many-body scar states considering a spin-1/2 many-body Hamiltonian describing a generalized Fredkin spin chain. We show that both scar states and weak fragmentation of the Hilbert space survive for almost any range of the coupling. Finally we investigate the effects of such structures of the Hilbert space on the out-of-equilibrium dynamics, triggered by certain initial states, characterized by either local persistent oscillations or non-uniform stationary profile of the magnetization.