Quantum simulation of Motzkin spin chain with Rydberg atoms

TL;DR

This paper proposes a Rydberg-atom quantum simulation scheme to realize the highly entangled Motzkin spin chain, enabling experimental exploration of complex topological phases with non-area-law entanglement.

Contribution

It introduces a practical method to simulate Motzkin spins using Rydberg atoms, bridging theoretical models and experimental quantum simulation.

Findings

Effective Motzkin ground state reproduces entanglement scaling

Simulation captures block-structure of the reduced density matrix

Pathway for experimental realization of exotic phases

Abstract

Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultra-cold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.