Thermal evolution of multipartite entanglement in a spin ½ antiferromagnetic Heisenberg chain system C14D18CuN4O10 via inelastic neutron scattering

Fisher information has been proposed to be a witness of m-particle multipartite entanglement and realized experimentally very recently via inelastic neutron scattering. The ground state of a spin ½ Heisenberg antiferromagnetic chain is a Tomonaga-Luttinger liquid (TLL) where quantum mechanical fluctuations do not allow for long range order even at T = 0 K. The excitation spectra of the TLL is gapless comprising spin ½ interacting fermions known as spinons. C14D18CuN4O10 has been shown to be an excellent realization of a TLL with an exchange coupling constant J/kB = 1.23 K. Through inelastic neutron scattering measurements done at different temperatures, we want to calculate the thermal evolution of the spinon spectra of C14D18CuN4O10 over the entire Brillouin zone. Using this, we want to observe the thermal evolution of multipartite entanglement via Fisher information and check the limit of multipartite entanglement to understand if exchange coupling constant protects thermal decoherence of the system. Consequently, entanglement teleportation fidelity temperature of the system will be estimated.