Energy as witness of multipartite entanglement in spin clusters

TL;DR

This paper establishes energy-based criteria to detect multipartite entanglement in spin clusters, deriving bounds and demonstrating that ground states of Heisenberg chains are genuinely entangled.

Contribution

It introduces a method to identify multipartite entanglement using energy minima in spin systems with arbitrary spins up to 5/2, extending entanglement detection techniques.

Findings

Ground states of Heisenberg chains are N-partite entangled.

Derived energy bounds serve as witnesses for multipartite entanglement.

Computed energy gaps for chains with up to 8 spins.

Abstract

We derive energy minima for biseparable states in three- and four-spin systems, with Heisenberg Hamiltonian and s <= 5/2. These provide lower bounds for tripartite and quadripartite entanglement in chains and rings with larger spin number N. We demonstrate that the ground state of an $N$-spin Heisenberg chain is $N$-partite entangled, and compute the energy gap with respect to biseparable states for N <= 8.