Characterizing and Quantifying Frustration in Quantum Many-Body Systems

TL;DR

This paper introduces a universal measure of frustration in quantum many-body systems, relating it to entanglement and providing criteria to identify geometrically unfrustrated models with purely quantum frustration.

Contribution

It proposes a general scheme for quantifying quantum frustration, introduces conditions for inequality saturation, and links frustration to entanglement in quantum systems.

Findings

Established a universal frustration measure for quantum systems.

Derived conditions for inequality saturation in quantum spin models.

Validated conditions through extensive numerical tests.

Abstract

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.