The Interplay between Frustration and Entanglement in Many-Body Systems

TL;DR

This paper investigates the relationship between frustration, entanglement, and degeneracy in quantum many-body systems with Heisenberg-like interactions, developing tools to analyze their interplay and refining classification methods.

Contribution

It introduces analytical and numerical tools to quantify the interplay between frustration, entanglement, and degeneracy, and refines the quantum Toulouse conditions for classifying many-body systems.

Findings

Quantum Toulouse conditions effectively classify systems

Local ground states influence frustration and entanglement interplay

Refinements to existing classification criteria are proposed

Abstract

Frustration of classical many-body systems can be used to distinguish ferromagnetic interactions from anti-ferromagnetic ones via the Toulouse conditions. A quantum version of the Toulouse conditions provides a similar classification based on the local ground states. We compute the global ground states for a family of models with Heisenberg-like interactions and analyse their behaviour with respect to frustration, entanglement and degeneracy. For that we develop analytical and numerical analysing tools capable to quantify the interplay between those three quantities. We find that the quantum Toulouse conditions provide a proper classification, however, refinements can be found. Our results show how the different local ground states affect the interplay and pave the way for further generalisation and possible applications to other quantum many-body systems.