Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions

TL;DR

This paper explores quantum frustration in many-body systems, linking it to entanglement and monogamy constraints, and identifies observable signatures of quantum versus classical frustration transitions.

Contribution

It introduces a universal measure of quantum frustration based on incompatibility and entanglement, and analyzes frustration transitions in spin models with competing interactions.

Findings

Valence bond solids indicate a transition from classical to quantum frustration.

Quantum frustration is related to non-commutativity of local interactions.

Observable quantities can detect frustration transitions.

Abstract

Frustration in quantum many body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, to the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated to exact ground-state dimerization correspond to a transition from generic frustration, i.e. geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e. solely due to the non-commutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.