Quantum many-body entanglement is a pervasive theme in modern physics, and it represents the key aspect underlying the complexity of quantum matter. Detecting many-body entanglement (e.g. via entanglement entropies) in experiments has become possible in artificial quantum systems, such as small assemblies of cold atoms or trapped ions. But it remains much harder (if not impossible) in bulk quantum matter, whose characterization is still largely based on concepts possessing a classical analog. A paradigm shift for entanglement detection in quantum matter is nonetheless offered by quantum coherence estimators — such as the quantum Fisher information — characterizing the fact that an observable does not commute with the quantum state of interest. In equilibrium quantum matter, many-body quantum coherence can be reconstructed from the nonlocal dynamical response of the system, probed e.g. via neutron scattering.
I will illustrate the simplest quantum coherence measure — dubbed quantum variance [1] — which has an immediate thermodynamic significance: the difference between the fluctuations of quantity and its iso-thermal susceptibility. I will illustrate how this quantum coherence measure can be used theoretically to detect a fundamental, yet elusive quantum trait in the thermodynamics of quantum matter, namely the occurrence of a quantum critical fan above a zero-temperature quantum critical point [2]. I will discuss how recent neutron scattering experiments [3] were able to fully reconstruct the spatial structure of quantum coherence and entanglement in a system of coupled Heisenberg chains, exhibiting a fundamental decay length (the quantum coherence length) of purely quantum-mechanical origin [4]; and how the spatial structure of quantum correlations can possess a very special, “monogamous" nature [3], suggesting a special role for low-dimensional quantum materials.
[1] I. Frérot and T. Roscilde. Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems. Phys. Rev. B, 94:075121 (2016).
[2] I. Frérot and T. Roscilde. Reconstructing the quantum critical fan of strongly correlated systems using quantum correlations. Nature Communications, 10(1):577 (2019).
[3] A. Scheie, P. Laurell, E. Dagotto, D. A. Tennant, and T. Roscilde. Reconstructing the spatial structure of quantum correlations, arXiv 2023.
[4] D. Malpetti and T. Roscilde. Quantum correlations, separability, and quantum coherence length in equilibrium many-body systems. Phys. Rev. Lett., 117:130401 (2016).
