# Dynamics and correlations in Motzkin and Fredkin spin chains

## TL;DR

This paper investigates the quantum dynamical behavior of Motzkin and Fredkin spin chains after a quench, analyzing how excitations evolve and correlations decay, revealing unusual properties related to entanglement and correlation functions.

## Contribution

It provides a detailed analysis of the time evolution of excitations and correlations in Motzkin and Fredkin chains, highlighting their anomalous dynamical behaviors.

## Key findings

- Unusual correlation decay patterns observed
- Violation of cluster decomposition property identified
- Distinct dynamical responses compared to typical spin chains

## Abstract

The Motzkin and Fredkin quantum spin chains are described by frustration-free Hamiltonians recently introduced and studied because of their anomalous behaviors in the correlation functions and in the entanglement properties. In this paper we analyze their quantum dynamical properties, focusing in particular on the time evolution of the excitations driven by a quantum quench, looking at the correlations functions of spin operators defined along different directions, and discussing the results in relation with the cluster decomposition property.