Frustration, Entanglement, and Correlations in Quantum Many Body Systems

TL;DR

This paper derives an exact lower bound for frustration in quantum many-body systems, linking it to entanglement and classical correlations, and explores conditions for saturation and degeneracy effects.

Contribution

It introduces a universal lower bound on frustration in degenerate ground states, connecting it to entanglement and classical correlations, with conditions for saturation.

Findings

Lower bound on frustration derived

Frustration linked to entanglement and classical correlations

Saturation conditions identified for certain models

Abstract

We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.