The Hubbard model describes interacting itinerant fermion systems and is the simplest model capable of describing the essential physics of strongly correlated electron systems. In this model, both spin correlations and charge correlations are important for the entanglement, thus the magnetic susceptibility is not an appropriate thermal entanglement witness. The specific heat reflects spin correlations and charge correlations. We obtain a relation that permits the specific heat to be used directly as a thermal entanglement witness. We calculate, away from half filling, the entanglement critical temperature
TE, below which entanglement is detected, for small linear clusters and the hypercubic lattice in the limit of infinite dimensions by using the exact numerical diagonalization method and the dynamical mean-field theory, respectively. We find, in both cases, that
TE increases with increasing strength of the on-site Coulomb repulsion
U.
The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound
Na2Cu5Si4O14. The presence of entanglement was investigated through two measured quantities, an entanglement witness and the entanglement of formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below $\ensuremath{\sim}200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Tripartite entanglement was also observed below $\ensuremath{\sim}240\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.
The present work reports an experimental observation of thermal entanglement in a clusterized spin chain formed in the compound Na2Cu5Si4O14. The presence of entanglement was investigated through two measured quantities, an entanglement witness and the entanglement of formation, both derived from the magnetic susceptibility. It was found that pairwise entanglement exists below 200 K. Tripartite entanglement was also observed below 240 K. A theoretical study of entanglement evolution as a function of applied field and temperature is also presented.
We study quantum entanglement in half-filled Hubbard dimers at finite temperatures under an external magnetic field. Due to the itinerant nature of the electrons and their fundamental indistinguishability, we employ a site-based evaluation of entanglement via the concurrence in three distinct sectors of the Hilbert space, namely the charge, zero-, and single-spin subspaces. At zero temperature these measures can be combined to produce an accurate estimate of the entanglement entropy. For finite temperatures we show that those concurrences display reentrant behavior upon varying the magnetic field. Furthermore, we unveil that charge and spin quantum correlations are quite distinctly degraded by thermal fluctuations.
In the present work, we investigate the quantum thermal entanglement in molecular magnets composed of dimers of spin S , using an Entanglement Witness built from measurements of magnetic susceptibility. An entanglement temperature, T e , is then obtained for some values of spin S . From this, it is shown that T e is proportional to the intradimer exchange interaction J and that entanglement appears only for antiferromagnetic coupling. The results are compared to experiments carried on three isostructural materials: KNaMSi 4 O 10 (M=Mn, Fe or Cu).
Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude
21, in which the spins interact via nearest-neighbor, diagonal, and four-spin interactions of strength
J1,
J2, and
K, respectively. The ground- and thermal-state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Both bipartite and multipartite entanglements are considered and a signature of the quantum phase transition (QPT), in terms of the entanglement ratio, is identified. The first-order QPT is accompanied by discontinuities in the nearest-neighbor and diagonal concurrences. The magnetic properties of a
S=21 antiferromagnetic polyoxovanadate compound V12 are well explained by tetramers, with
J2=0,
K=0, in which the spins interact via the isotropic Heisenberg exchange interaction Hamiltonian. Treating the magnetic susceptibility $\ensuremath{\chi}$ as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature
Tc below which entanglement is present in the experimental compound, is determined. Two other cases considered include the symmetric tetramer---i.e., tetrahedron
(J1=J2,K=0)---and the symmetric trimer. In both the cases, there is no entanglement between a pair of spins in the thermal state but multipartite entanglement is present. A second EW based on energy provides an estimate of the entanglement temperature
TE below which the thermal state is definitely entangled. This EW detects bipartite entanglement in the case of the tetramer describing a square of spins (the case of V12 ) and multipartite entanglement in the cases of the tetrahedron and symmetric trimer.