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arXiv:2306.11723

Reconstructing the spatial structure of quantum correlations in materials

Allen O. Scheie, Pontus Laurell, Elbio R. Dagotto, D. M. Tennant, Tommaso Roscilde

Published Jun 20, 2023• 0 citations
arXivHTMLPDF

Abstract

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 KCuF$_3$ $\unicode{x2014}$ a system of weakly coupled $S=1/2$ 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.

DOI
10.48550/arxiv.2306.11723

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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​ \unicodex2014\unicode{x2014}\unicodex2014 a system of weakly coupled S=1/2S=1/2S=1/2 Heisenberg chains \unicodex2014\unicode{x2014}\unicodex2014 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 \unicodex2014\unicode{x2014}\unicodex2014 the quantum coherence length \unicodex2014\unicode{x2014}\unicodex2014 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.
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
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.
The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wave vector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time, and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.
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.
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​.
Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform quantitatively reliable material simulations. We demonstrate that a superconducting quantum processor operating on up to 50 qubits can already produce meaningful, quantitative comparisons with inelastic neutron-scattering measurements of KCuF3_33​, a canonical realization of a gapless Luttinger liquid system with a strongly correlated ground state and a spectrum of emergent spinons. The quantum simulation is enabled by a quantum-classical workflow for computing dynamical structure factors (DSFs). The resulting spectra are benchmarked against experimental measurements using multiple metrics, highlighting the impact of circuit depth and circuit fidelity on simulation accuracy. Finally, we extend our simulations to a 1D XXZ Heisenberg model with next-nearest-neighbor (NNN) interactions and a strong anisotropy, producing a gapped excitation spectrum, which could be used to describe the CsCoX3_33​ compounds above the Néel temperature. Our results establish a framework for computing DSFs for quantum materials in classically challenging regimes of strong entanglement and long-range interactions, enabling quantum simulations that are directly testable against laboratory measurements.