Deformed Fredkin Spin Chain with Extensive Entanglement

TL;DR

This paper introduces a deformed Fredkin spin chain with a phase transition in entanglement entropy scaling, demonstrating bounded and extensive entanglement regimes depending on local degrees of freedom.

Contribution

It presents a new spin chain model with a tunable phase transition in entanglement entropy, expanding understanding of entanglement scaling in quantum spin systems.

Findings

In the spin 1/2 case, entanglement obeys an area law with bounded entropy.

Introducing color degrees of freedom leads to linear, volume-like entanglement scaling.

The model provides a new example of a critical phase with extensive entanglement entropy.

Abstract

We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths. In the purely spin $1/2$ case, the entanglement entropy obeys an area law: it is bounded from above by a constant, when the size of the block $n$ increases (and $t>1$). When a local color degree of freedom is introduced the entanglement entropy increases linearly with the size of the block (and $t>1$). The entanglement entropy of half of the chain is tightly bounded by ${ n}\log s$ where $n$ is the size of the block, and $s$ is the number of colors. Our chain fosters a new example for a significant boost to entropy and for the existence of the associated critical rainbow phase where the entanglement entropy scales with volume that has recently been discovered in Zhang et al. (arXiv:1606.07795)