Experimental evaluation of quantum entanglement measures in spin chain systems

Fractionalized excitations in quantum magnets such as 1D Heisenberg S=1/2 systems (quantum spin chains) are known to present evidence of quantum entangled states. Conventionally, systems with larger angular momenta (S≥3/2) are closer to the classical limit and therefore quantum entanglement is less important. Some rare earth systems nevertheless exhibit S=1/2 physics due to the selection of ground-state Kramers doublets by strong spin-orbit coupling and crystal electric fields. Here we present analysis of inelastic neutron scattering experiments, aiming to evaluate how the prevalence of quantum collective behavior (multipartite entanglement) manifests itself in the effective S=1/2 case of a rare earth Yb ion. We turn to recent advances to the analysis of neutron spectra, which have shown it possible to calculate certain model-independent measures of multipartite entanglement. These entanglement measures, such as the quantum Fisher information, can place quantitative bounds on the degree of entanglement which may be present in a system. These have already been evaluated by others on KuCF₃ [1], a system of weakly coupled S=1/2 chains. Here, we analyze entanglement measures in a rare earth material YbAlO₃[2], which demonstrates clear two-spinon spectra characteristic of quantum spin chains and compare it with the case of a higher-spin transition metal system. Special attention is paid to the behavior of these entanglement measures at magnetic field and temperature points near known thermal and quantum phase transitions.



References:

[1] A. Scheie, Pontus Laurell, A. M. Samarakoon, B. Lake, S. E. Nagler, G. E. Granroth, S. Okamoto, G. Alvarez, D. A. Tennant. Witnessing entanglement in quantum magnets using neutron scattering. Phys. Rev. B 103, 224434 (2021).

[2] L. S. Wu, S. E. Nikitin, Z. Wang, W. Zhu, C. D. Batista, A. M. Tsvelik, A. M. Samarakoon, D. A. Tennant, M. Brando, L. Vasylechko, M. Frontzek, A. T. Savici, G. Sala, G. Ehlers, A. D. Christianson, M. D. Lumsden, A. Podlesnyak, Tomonaga–Luttinger liquid behavior and spinon confinement in YbAlO3, Nature Comm., 10, 698 (2019).