Witnessing entanglement in quantum magnets using neutron scattering

A. Scheie; Pontus Laurell; A. M. Samarakoon; B. Lake; S. E. Nagler; G. E. Granroth; S. Okamoto; G. Alvarez; D. A. Tennant

doi:10.1103/PhysRevB.103.224434

Witnessing entanglement in quantum magnets using neutron scattering

A. Scheie, Pontus Laurell, A. M. Samarakoon, B. Lake, S. E. Nagler, G. E. Granroth, S. Okamoto, G. Alvarez, D. A. Tennant

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We demonstrate how quantum entanglement can be directly witnessed in the quasi-1D Heisenberg antiferromagnet KCuF3. We apply three entanglement witnesses - one tangle, two tangle, and quantum Fisher information - to its inelastic neutron spectrum and compare with spectra simulated by finite-temperature density matrix renormalization group (DMRG) and classical Monte Carlo methods. We find that each witness provides direct access to entanglement. Of these, quantum Fisher information is the most robust experimentally and indicates the presence of at least bipartite entanglement up to at least 50 K, corresponding to around 10% of the spinon zone-boundary energy. We apply quantum Fisher information to higher spin-S Heisenberg chains and show theoretically that the witnessable entanglement gets suppressed to lower temperatures as the quantum number increases. Finally, we outline how these results can be applied to higher dimensional quantum materials to witness and quantify entanglement.

Original language	English
Article number	224434
Journal	Physical Review B
Volume	103
Issue number	22
DOIs	https://doi.org/10.1103/PhysRevB.103.224434
State	Published - Jun 1 2021

Funding

We gratefully acknowledge Jean-Sébastien Caux for performing the Bethe ansatz calculations in Ref. . We thank Matthew Stone for a critical reading of the manuscript. D.A.T. acknowledges stimulating and useful discussions with Cristian Batista, Gábor Halász, Pavel Lougovski, Gerardo Ortiz, and Roger Pynn. The research by P.L., S.O., and G.A. was supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences, Division of Materials Sciences and Engineering. G.A. was in part supported by the ExaTN ORNL LDRD. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The work by DAT and SEN is supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE). Software development has been partially supported by the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

Funders	Funder number
Center for Nanophase Materials Sciences
National Quantum Information Science Research Center
ORNL LDRD
Quantum Science Center
U.S. Department of Energy
Office of Science
Advanced Scientific Computing Research
Division of Materials Sciences and Engineering

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10.1103/PhysRevB.103.224434

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abstract = "We demonstrate how quantum entanglement can be directly witnessed in the quasi-1D Heisenberg antiferromagnet KCuF3. We apply three entanglement witnesses - one tangle, two tangle, and quantum Fisher information - to its inelastic neutron spectrum and compare with spectra simulated by finite-temperature density matrix renormalization group (DMRG) and classical Monte Carlo methods. We find that each witness provides direct access to entanglement. Of these, quantum Fisher information is the most robust experimentally and indicates the presence of at least bipartite entanglement up to at least 50 K, corresponding to around 10% of the spinon zone-boundary energy. We apply quantum Fisher information to higher spin-S Heisenberg chains and show theoretically that the witnessable entanglement gets suppressed to lower temperatures as the quantum number increases. Finally, we outline how these results can be applied to higher dimensional quantum materials to witness and quantify entanglement.",

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AU - Laurell, Pontus

AU - Samarakoon, A. M.

AU - Lake, B.

AU - Nagler, S. E.

AU - Granroth, G. E.

AU - Okamoto, S.

AU - Alvarez, G.

AU - Tennant, D. A.

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AB - We demonstrate how quantum entanglement can be directly witnessed in the quasi-1D Heisenberg antiferromagnet KCuF3. We apply three entanglement witnesses - one tangle, two tangle, and quantum Fisher information - to its inelastic neutron spectrum and compare with spectra simulated by finite-temperature density matrix renormalization group (DMRG) and classical Monte Carlo methods. We find that each witness provides direct access to entanglement. Of these, quantum Fisher information is the most robust experimentally and indicates the presence of at least bipartite entanglement up to at least 50 K, corresponding to around 10% of the spinon zone-boundary energy. We apply quantum Fisher information to higher spin-S Heisenberg chains and show theoretically that the witnessable entanglement gets suppressed to lower temperatures as the quantum number increases. Finally, we outline how these results can be applied to higher dimensional quantum materials to witness and quantify entanglement.

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Witnessing entanglement in quantum magnets using neutron scattering

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