Macroscopic inequivalent entanglement witness in Heisenberg spin chain

Motivated by the wise idea of entanglement witness (EW), we present an inequivalent entanglement witness (IEEW) that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication (SLOCC) in the Heisenberg spin chain. Since the IEEW is the absolute value of magnetization |M| that is a macroscopically measurable quantity, our conclusions provide a macroscopic method to detect inequivalent entanglement between microscopic spins, on the one hand, and clearly show that inequivalent entanglement can yield different macroscopic effects, on the other hand.