Four interacting spins: addition of angular momenta, spin-spin correlation functions, and entanglement

TL;DR

This paper analyzes a four-spin ring with competing interactions, revealing how the ground state, correlations, and entanglement evolve with interaction strength using angular momentum addition rules.

Contribution

It introduces a simple method based on angular momentum addition to study the spectrum and entanglement in a four-spin system with competing interactions.

Findings

Ground state evolution characterized by level crossings

Spin-spin correlation functions vary with interaction parameter

Entanglement entropy depends on system partitioning

Abstract

We study four spins on a ring coupled through competing Heisenberg interactions between nearest neighbors, $J$, and next-nearest neighbors, $J_2\equiv\alpha J>0$. The spectrum is obtained in a simple way by using the rules for addition of 4 angular momenta. This allows us to follow the evolution of the ground state with $\alpha$, characterized by level crossings and by analyses of spin-spin correlation functions. Further insight is obtained by examining the entanglement between different parts of the system: we observe that the entanglement entropy is strongly dependent on how the system is partitioned.