Dimensionality induced entanglement in macroscopic dimer systems

TL;DR

This paper explores how the entanglement between neighboring spins in lattice systems depends on the spin value and dimensionality, revealing a threshold behavior in higher dimensions.

Contribution

It introduces a novel analysis of entanglement in dimer coverings across arbitrary lattice topologies and dimensions, highlighting the impact of spin and dimensionality.

Findings

Nearest neighbor entanglement exists for any spin in 1D.

In higher dimensions, a spin threshold exists below which entanglement vanishes.

Large spin limit corresponds to maximum nearest neighbor entanglement.

Abstract

We investigate entanglement properties of mixtures of short-range spin-s dimer coverings in lattices of arbitrary topology and dimension. We show that in one spacial dimension nearest neighbour entanglement exists for any spin $s$. Surprisingly, in higher spatial dimensions there is a threshold value of spin $s$ below which the nearest neighbour entanglement disappears. The traditional "classical" limit of large spin value corresponds to the highest nearest neighbour entanglement that we quantify using the negativity.