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Physical review. B./Physical review. B

Multipartite entanglement in the one-dimensional spin- 1 2 Heisenberg antiferromagnet

Varun Menon, Nicholas E. Sherman, Maxime Dupont, Allen O. Scheie, D. M. Tennant, Joel E. Moore

Published Feb 17, 2023• 19 citations
Publisher

Abstract

Multipartite entanglement was thought to be intrinsically difficult to measure in solids, but recent work has established connections between multipartite entanglement, dynamic susceptibilities, and neutron scattering data, via the quantum Fisher information. This work focuses on the paradigmatic spin-half chain and shows that there are further simplifications: even static structure factors contain quantitative information about multipartite entanglement at low temperatures. Theory, numerics, and experiment then suggest that a high degree of multipartite entanglement is observable in Heisenberg chain compounds, including KCuF${}_{3}$.

DOI
10.1103/physrevb.107.054422

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IEEE Transactions on Magnetics•Mar 25, 2026•0 citations
Multipartite entanglement was thought to be intrinsically difficult to measure in solids, but recent work has established connections between multipartite entanglement, dynamic susceptibilities, and neutron scattering data, via the quantum Fisher information. This work focuses on the paradigmatic spin-half chain and shows that there are further simplifications: even static structure factors contain quantitative information about multipartite entanglement at low temperatures. Theory, numerics, and experiment then suggest that a high degree of multipartite entanglement is observable in Heisenberg chain compounds, including KCuF3{}_{3}3​.
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Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the Quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as T→0T\rightarrow 0T→0. We argue that this implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale that is determined by universal properties, up to a non-universal amplitude. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges non-trivially as ∼log⁡(1/T)3/2\sim \log(1/T)^{3/2}∼log(1/T)3/2. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF3_33​, a material well-described by the Heisenberg chain.
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This tutorial is a pedagogical introduction to recent methods of computing quantum spin entanglement witnesses from spectroscopy, with a special focus on neutron scattering on quantum spin systems. We offer a brief introduction to the concepts and equations, define a data analysis protocol, and discuss the interpretation of three entanglement witnesses: one-tangle, two-tangle, and Quantum Fisher Information . We also discuss practical experimental considerations, and give three examples of extracting entanglement witnesses from experimental data: Copper Nitrate, KCuF 3 , and NiPS 3 .
This study presents a rigorous analysis of the temperature and the magnetic field dependence of the dynamical autocorrelations and correlation functions in the spin-1/2 Heisenberg tetrahedron. Exact results for these quantities are employed to evaluate the corresponding static and dynamic structure factors, which can be directly probed through inelastic neutron scattering experiments. It is demonstrated that the combination of inelastic neutron scattering data with basic magnetometry measurements enables the extraction of the concurrence serving as a quantitative measure of bipartite entanglement. Notably, pronounced temperature-induced variations in both structure factors and concurrence emerge near two level-crossing fields associated with field-driven transitions between singlet–triplet and triplet–quintet ground states.