Topological Non--connectivity Threshold in long-range spin systems

TL;DR

This paper investigates the topological disconnection threshold in one-dimensional anisotropic Heisenberg models with long-range interactions, revealing how the threshold behaves depending on the interaction decay rate and system dimension.

Contribution

It demonstrates the existence of a topological disconnection threshold in long-range spin systems and analyzes its dependence on the decay exponent and system dimension.

Findings

Disconnection threshold exists for certain long-range interactions.

The ratio of disconnected energy to total energy varies with interaction decay rate.

Numerical simulations support the persistence of the threshold in higher dimensions.

Abstract

We demonstrate the existence of a topological disconnection threshold, recently found in Ref. \cite{JSP}, for generic $1-d$ anisotropic Heisenberg models interacting with an inter--particle potential $R^{-\alpha}$ when $0<\alpha < 1$ (here $R$ is the distance among spins). We also show that if $\alpha $ is greater than the embedding dimension $d$ then the ratio between the disconnected energy region and the total energy region goes to zero when the number of spins becomes very large. On the other hand, numerical simulations in $d=2,3$ for the long-range case $\alpha < d$ support the conclusion that such a ratio remains finite for large $N$ values. The disconnection threshold can thus be thought as a distinctive property of anisotropic long-range interacting systems.