Onofre Rojas

Thermal entanglement of a spin-1/2 Ising–Heisenberg model on a symmetrical diamond chain

The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.

Exactly solvable mixed-spin Ising-Heisenberg diamond chain with biquadratic interactions and single-ion anisotropy

An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the

Frustrated Ising model on the Cairo pentagonal lattice.

T=0

Pairwise thermal entanglement in the Ising-XYZ diamond chain structure in an external magnetic field

ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. nSolving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link).

Spinless fermion model on diamond chain

Through the direct decoration transformation approach, we obtain a general solution for the pentagonal Ising model, showing its equivalence to the isotropic free-fermion eight-vertex model. We study the ground-state phase diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state, and one frustrated state are found. Using the exact solution of the pentagonal Ising model, we discuss the finite-temperature phase diagrams and find a phase transition between the FIM state and the disordered state as well as a phase transition between the disordered state and the FM state. We also discuss some additional remarkable properties of the model, such as the magnetization, entropy, and specific heat, at finite temperature and at its low-temperature asymptotic limit. Because of the influence of the second-order phase transition between the frustrated and ferromagnetic phases, we obtain surprisingly low values of the entropy and the specific heat until the critical temperature is reached.

Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain.

Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a rich entanglement feature, due to the fact that the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss the two-qubit thermal entanglement effect on the Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements; using this result we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, e.g., the boundary of two entangled regions becomes a disentangled region, and this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Although a similar property had been found for only two qubits, here we show it for the case of a diamond chain structure, which reasonably represents real materials.

Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit.

Abstract The decoration or iteration transformation were widely applied to solve exactly the magnetic spin models in one-dimensional and two-dimensional lattice. The motif of this Letter is to extend the decoration transformation approach for models that describe interacting electron systems instead of spin magnetic systems, one illustrative model to be studied, will be the spinless fermion model on diamond chain. Using the decoration transformation, we are able to solve this model exactly. The phase diagram of this model was explored at zero temperature as well as the thermodynamic properties of the model for any particle density. The particular case when particle–hole symmetry is satisfied was also discussed.

Spin frustration of a spin-1/2 Ising–Heisenberg three-leg tube as an indispensable ground for thermal entanglement

The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.

Two-dimensional XXZ -Ising model on a square-hexagon lattice.

We study the geometrical frustration of an extended Hubbard model on a diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites while the remaining lines represent only the Coulomb repulsion term. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of nonfrustrated states, ordered antiferromagnetically. Although a decoration transformation was derived for spin-coupling systems, this approach can be applied to electron-coupling systems. Thus the extended Hubbard model can be mapped onto another effective extended Hubbard model in the atomic limit with additional three- and four-body couplings. This effective model is solved exactly using the transfer-matrix method. In addition, using the exact solution of this model, we discuss several thermodynamic properties away from the half-filled band, such as chemical potential behavior, electronic density, and entropy, for which we study geometrical frustration. Consequently, we investigate the specific heat as well.

High-temperature series expansion of the Helmholtz free energy of the quantum spin- S X Y Z chain

Abstract The spin-1/2 Ising–Heisenberg three-leg tube composed of the Heisenberg spin triangles mutually coupled through the Ising inter-triangle interaction is exactly solved in a zero magnetic field. By making use of the local conservation for the total spin on each Heisenberg spin triangle the model can be rigorously mapped onto a classical composite spin-chain model, which is subsequently exactly treated through the transfer-matrix method. The ground-state phase diagram, correlation functions, concurrence, Bell function, entropy and specific heat are examined in detail. It is shown that the spin frustration represents an indispensable ground for a thermal entanglement, which is quantified by the quantum concurrence. The specific heat displays diverse temperature dependences, which may include a sharp low-temperature peak mimicking a temperature-driven first-order phase transition. It is convincingly evidenced that this anomalous peak originates from massive thermal excitations from the doubly degenerate ground state towards an excited state with a high macroscopic degeneracy due to chiral degrees of freedom of the Heisenberg spin triangles.