Thermal entanglement between non-nearest-neighbor spins on fractal lattices

TL;DR

This study explores how thermal entanglement between non-nearest-neighbor spins varies with temperature, anisotropy, and system size on fractal lattices, revealing that fractal structure influences entanglement robustness.

Contribution

It introduces a decimation RG method to analyze thermal entanglement on fractal lattices, highlighting the impact of fractal geometry on entanglement stability and size dependence.

Findings

Entanglement decreases with temperature and vanishes beyond T_c.

Entanglement first increases then sharply decreases with anisotropy parameter Δ.

Entanglement is fragile in chains and Koch curves but robust in certain hierarchical lattices.

Abstract

We investigate thermal entanglement between two non-nearest-neighbor sites in ferromagnetic Heisenberg chain and on fractal lattices by means of the decimation renormalization-group (RG) method. It is found that the entanglement decreases with increasing temperature and it disappears beyond a critical value T_{c}. Thermal entanglement at a certain temperature first increases with the increase of the anisotropy parameter {\Delta} and then decreases sharply to zero when {\Delta} is close to the isotropic point. We also show how the entanglement evolves as the size of the system L becomes large via the RG method. As L increases, for the spin chain and Koch curve the entanglement between two terminal spins is fragile and vanishes when L\geq17, but for two kinds of diamond-type hierarchical (DH) lattices the entanglement is rather robust and can exist even when L becomes very large. Our result indicates that the special fractal structure can affect the change of entanglement with system size.