Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S=1/2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement.
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.
Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.
The paper reports a computational study of the quantum entanglement in V12 cluster molecular magnet. The low-temperature properties of the system are modelled with anisotropic quantum Heisenberg model on a tetramer of spins S=1/2 in the external magnetic field. The two-spin entanglement is quantified using the concurrence, whereas the fidelity serves as a measure of four-spin entanglement. The analytic and numerical results are derived and discussed, emphasizing the importance of real-space and spin-space interaction anisotropy and the role of quantum level crossings in the entanglement description in V12.
The energy spectrum, ground-state phase diagram, pair correlation functions, and concurrence are exactly calculated for a spin-1/2 quantum Heisenberg distorted tetrahedron in a magnetic field.The ground-state phase diagram in the interaction ratio versus magnetic field plane totally involves five different ground states, which differ from one another by the total spin, local pair correlation functions, and/or concurrence.In addition to the classical fully polarized ferromagnetic ground state there also appear four outstanding quantum ground states, two of which belong to a singlet sector and another two to a triplet sector.A degree of bipartite entanglement quantified through the concurrence is examined as a function of magnetic field, temperature, and the interaction ratio.
The magnetic and thermodynamic properties of 13-atom clusters with decahedral and layered geometries have been studied with spin-1/2 using the quantum Heisenberg model. The numerical exact diagonalization technique is applied to solve the quantumspin Hamiltonian for both ferro (FM) and anti-ferromagnetic (AFM) interactions of the clusters. The ground state energies for the FM case are found to be all degenerate while for the AFM case, they are non-degenerate. In the presence of external magnetic field, we found discontinuities in the field-dependent magnetization accompanied by plateaus for the AFM interaction. The thermodynamic entities such as entropy and specific heat as a function of external magnetic field are smeared out with increasing temperature. They also show a strong dependence on the cluster geometry.
We study a spin-1/2 model with triangular
XXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate ``classical'' Ising spins. Diagonalization of the triangular
XXZ clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization
M equal to fractions 0,
1/4, and
1/2 of the saturation magnetization
M=1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of
T=0 magnetization curves, entropy as a function of temperature
T and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu
2(BO
3)
2.