Multipartite entanglement in the one-dimensional spin- 12 Heisenberg antiferromagnet

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

doi:10.1103/physrevb.107.054422

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

Journal Article · Fri Feb 17 00:00:00 EST 2023 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.107.054422· OSTI ID:2229875

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University of California, Berkeley, CA (United States)
University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). Materials Sciences Division
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
University of Tennessee, Knoxville, TN (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

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→0. This implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale of the system. 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. Furthermore, the 1D spin- 1 2 antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges nontrivially as ~ln(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, a material well described by the Heisenberg chain.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: AC02-05CH11231; DMR-1918065

OSTI ID:: 2229875

Journal Information:: Physical Review. B, Vol. 107, Issue 5; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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