S. M. de Souza

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

Phase diagram of the asymmetric tetrahedral Ising-Heisenberg chain

T=0

Thermal entanglement in an exactly solvable Ising-XXZdiamond chain structure

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. Solving 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).

High Temperature Expansion for a Chain Model

The asymmetric tetrahedron is composed by all edges of tetrahedron represented by Ising interaction except one, which has a Heisenberg type interaction. This asymmetric tetrahedron is arranged connecting a vertex which edges are only Ising type interaction to another vertex with same structure of another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising-Heisenberg chain. We have studied the ground state phase diagram for this kind of models. Particularly we consider two situations in the Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2) Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamics properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.

Direct algebraic mapping transformation for decorated spin models

Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.

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

We consider an arbitrary translationally invariant chain model with nearest neighbors interaction and satisfying periodic boundary condition. The approach developed here allows a thermodynamic description of the chain model directly in terms of grand potential per site. This thermodynamic function is derived from an auxiliary function constructed only from open connected subchains. In order to exemplify its application and how this approach works we consider the Heisenberg XXZ model. We obtain the coefficients of the high temperature expansion of the free energy per site of the model up to third order.

Spinless fermion model on diamond chain

In this article we propose a general transformation for decorated spin models. The advantage of this transformation is to perform a direct mapping of a decorated spin model onto another effective spin thus simplifying algebraic computations by avoiding the proliferation of unnecessary iterative transformations and parameters that might otherwise lead to transcendental equations. Direct mapping transformation is discussed in detail for decorated Ising spin models as well as for decorated Ising-Heisenberg spin models, with arbitrary coordination number and with some constrained Hamiltonians parameter for systems with coordination number larger than 4 (3) with (without) spin inversion symmetry respectively. In order to illustrate this transformation we give several examples of this mapping transformation, where most of them were not explored yet.

Thermal entanglement in an orthogonal dimer-plaquette chain with alternating Ising-Heisenberg coupling.

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.

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

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.

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

In this paper we explore the entanglement in an orthogonal dimer-plaquette Ising-Heisenberg chain, assembled between plaquette edges, also known as orthogonal dimer plaquettes. The quantum entanglement properties involving an infinite chain structure are quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by infinite chains. Using the local gauge symmetry of this model, we are able to map onto a simple spin-1 like Ising and spin-1/2 Heisenberg dimer model with single effective ion anisotropy. Thereafter this model can be solved using the decoration transformation and transfer matrix approach. First, we discuss the phase diagram at zero temperature of this model, where we find five ground states, one ferromagnetic, one antiferromagnetic, one triplet-triplet disordered and one triplet-singlet disordered phase, beside a dimer ferromagnetic-antiferromagnetic phase. In addition, we discuss the thermodynamic properties such as entropy, where we display the residual entropy. Furthermore, using the nearest site correlation function it is possible also to analyze the pairwise thermal entanglement for both orthogonal dimers. Additionally, we discuss the threshold temperature of the entangled region as a function of Hamiltonian parameters. We find a quite interesting thin reentrance threshold temperature for one of the dimers, and we also discuss the differences and similarities for both dimers.