Frustration, solitons, and entanglement in spin chains

TL;DR

This paper investigates the effects of frustration on spin chains, revealing how solitons influence entanglement properties and uncovering a new extensive entanglement scaling law in strongly frustrated regimes.

Contribution

It introduces a perturbative approach to solitonic ground states in frustrated spin chains and uncovers a novel extensive entanglement scaling law under strong frustration.

Findings

Weak frustration causes algebraic violation of the area law for EE.

Strong frustration leads to an extensive EE scaling law.

Enhanced frustration increases nonlocal correlations despite reducing total correlations.

Abstract

Defects in frustrated antiferromagnetic spin chains are universally present in geometrically frustrated systems. We consider the defects of the one-dimensional, spin-$s$ XXZ chain with single-ion anisotropy on a periodic chain with $N$ sites that was famously studied by Haldane. For $N$ odd the antiferromagnetic model is frustrated, and the ground state must include a soliton defect. We consider the Heisenberg interaction perturbatively and determine the corresponding perturbative solitonic ground state. Then we compute the entanglement spectrum, entanglement entropy (EE), capacity of entanglement (CE), and spin correlations in the solitonic ground state. For weak frustration, we find an algebraic violation of the area law for the EE consistent with recent results on weakly frustrated chains. Our analysis then moves beyond the weak frustration regime, and we obtain a novel extensive scaling law for the EE when strong frustration prevails, signalling large entanglement, and failure of the quasiparticle interpretation in this regime. Enhanced frustration results in less total correlations, but relatively more nonlocal correlations.