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arXiv:2102.08376 · Physical review. B./Physical review. B

Witnessing entanglement in quantum magnets using neutron scattering

Allen O. Scheie, Pontus Laurell, Anjana Samarakoon, B. Lake, S. E. Nagler, Garrett E. Granroth, Satoshi Okamoto, G. Alvarez, D. M. Tennant

Published Jun 28, 2021• 86 citations
arXivHTMLPDF

Abstract

Measuring quantum entanglement in solid state systems has been a long-standing challenge. Here, the authors use three entanglement witnesses borrowed from quantum information theory to directly detect quantum entanglement in the 1D Heisenberg spin chain system KCuF${}_{3}$ using inelastic neutron scattering data. The results are validated using density matrix renormalization group calculations and show that model-independent measures of quantum spin entanglement are experimentally possible, as well as reveal which witnesses are more experimentally robust.

DOI
10.1103/physrevb.103.224434

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Measuring quantum entanglement in solid state systems has been a long-standing challenge. Here, the authors use three entanglement witnesses borrowed from quantum information theory to directly detect quantum entanglement in the 1D Heisenberg spin chain system KCuF3{}_{3}3​ using inelastic neutron scattering data. The results are validated using density matrix renormalization group calculations and show that model-independent measures of quantum spin entanglement are experimentally possible, as well as reveal which witnesses are more experimentally robust.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
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 .
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​.
Heisenberg spin-1/2 chains are the archetype of quantum integrable one-dimensional models describing magnetic properties of a wide range of compounds (like the KCuF 3 crystal), which can be probed experimentally through neutron scattering experiments, while being at the same time at the root of the invention of Bethe ansatz and Yang-Baxter structures that led in turn to quantum groups discovery. The aim of this contribution is to describe these algebraic ingredients and to show how to obtain from them (using combined analytical and numerical analysis) dynamical correlation functions of integrable Heisenberg spin-1/2 chains, the Fourier transform of which, the so-called dynamical structure factors, being directly measured in inelastic neutron scattering experiments. Our method is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem. It leads to recent progress in the computation of integrable Heisenberg spin-1/2 chains correlation functions that we review here. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at an arbitrary mutual distance. Using neutron scattering data for the compound KCuF 3 —a system of weakly coupled S = 1 / 2 Heisenberg chains—and numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a different emergent length scale—the quantum coherence length—which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials. Published by the American Physical Society 2024
Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at arbitrary mutual distance. Using neutron scattering data on the compound KCuF3_33​ $\unicode{x2014}$ a system of weakly coupled S=1/2S=1/2S=1/2 Heisenberg chains $\unicode{x2014}$ and of numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a new emergent length scale $\unicode{x2014}$ the quantum coherence length $\unicode{x2014}$ which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials.