arXiv subjects

Onofre Rojas

Publications and source records attributed to Onofre Rojas.

At least 73 records · Page 4Linked to original sources

arXiv2012

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 the coupling constant values. Various regimes with different values of the 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.

cond-mat.str-el↗

arXiv2012

Geometrical frustration of an extended Hubbard diamond chain in the quasi-atomic limit

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

cond-mat.str-el↗

arXiv2012

Equivalence between non-bilinear spin-$S$ Ising model and Wajnflasz model

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-$S$ (for simplicity, we called as spin-$S$ polynomial) onto spin-crossover state. The spin-$S$ polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-$S$ is given by $2(2^{2S}-1)$. As an application of this mapping, we consider a general non-bilinear spin-$S$ Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-$S$ Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-$S$ Ising model.

cond-mat.stat-mech↗

arXiv2011

Spin-phonon coupling induced frustration in the exactly solved spin-1/2 Ising model on a decorated planar lattice

The spin-1/2 Ising model with a spin-phonon coupling on decorated planar lattices partially amenable to lattice vibrations is examined within the framework of the generalized decoration-iteration transformation and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective antiferromagnetic next-nearest-neighbour interaction, which competes with the nearest-neighbour interaction and is responsible for a frustration of the decorating spins. The strong enough spin-phonon coupling consequently leads to an appearance of the striking partially ordered and partially disordered phase, where a perfect antiferromagnetic alignment of the nodal spins is accompanied with a complete disorder of the decorating spins. The diversity in temperature dependences of the total specific heat is investigated in connection with the particular behaviour of its magnetic and lattice contribution.

cond-mat.stat-mech↗

arXiv2011

Bijection between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins $σ=\frac{p-1}{2}$

We propose a general method by which a spin-$S$ is decomposed into spins less than $S$. We have obtain the exact mapping between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins $σ=\frac{p-1}{2}$. We have discuss the possible applications of such transformations. In particular we have show how a general $d+1$ dimensional spin-$\frac{p-1}{2}$ model with general interactions can be reduced to $d$-dimensional spin-$S$ model with $S=\frac{p^{M}-1}{2}$.

math-ph↗

arXiv2011

Direct algebraic mapping transformation for decorated spin models

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 Hamiltonian's 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.

cond-mat.stat-mech↗

arXiv2011

A Frustrated 3-Dimensional Antiferromagnet: Stacked $J_{1}-J_{2}$ Layers

We study a frustrated 3D antiferromagnet of stacked $J_1 - J_2$ layers. The intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this there is a direct first-order transition from N{\' e}el to columnar order. Possible applications to real materials are discussed.

cond-mat.str-el↗

arXiv2010

Spinless fermion model on diamond chain

The decoration or iteration transformation was 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 thermodynamics properties of the model for any particle density. The particular case when particle-hole symmetry is satisfied was also discussed.

cond-mat.str-el↗

arXiv2010

Exactly solvable mixed-spin Ising-Heisenberg diamond chain with the 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 $T=0$ 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).

cond-mat.stat-mech↗

arXiv2009

A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the {\it free fermion} condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by $S+1/2$. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.

cond-mat.stat-mech↗

arXiv2009

Generalized Transformation for Decorated Spin Models

The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes $[-s,s]$ is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising models. We apply this transformation to a particular mixed spin-(1/2,1) and (1/2,2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-$S$ square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also include combinations of three-body and four-body interactions, particularly we considered spin 1 and 2.

math-ph↗

arXiv2008

Two dimensional XXZ-Ising model on square-hexagon lattice

We study a two dimensional XXZ-Ising on square-hexagon (4-6) lattice with spin-1/2. The phase diagram of the ground state energy is discussed, shown two different ferrimagnetic states and two type of antiferromagnetic states, beside of a ferromagnetic state. To solve this model, it could be mapped into the eight-vertex model with union jack interaction term. Imposing exact solution condition we find the region where the XXZ-Ising model on 4-6 lattice have exact solutions with one free parameter, for symmetric eight-vertex model condition. In this sense we explore the properties of the system and analyze the competition of the interaction parameters providing the region where it has an exact solution. However the present model does not satisfy the \textit{free fermion} condition, unless for a trivial situation. Even so we are able to discuss their critical points region, when the exactly solvable condition is ignored.

cond-mat.stat-mech↗

arXiv2008

Phase diagram of the asymmetric tetrahedral Ising-Heisenberg chain

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.

cond-mat.stat-mech↗

arXiv2006

The high temperature expansion of the classical $XYZ$ chain

We present the $β$-expansion of the Helmholtz free energy of the classical $XYZ$ model, with a single-ion anisotropy term and in the presence of an external magnetic field, up to order $β^{12}$. We compare our results to the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression for the thermodynamics of the $XXZ$ classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as $kT/J_x \approx 0.5$. We show that the specific heat and magnetic susceptibility of the spin-2 antiferromagnetic chain can be approximated by their respective classical results, up to $kT/J \approx 0.8$, within an error of 2.5%. In the absence of an external magnetic field, the ferromagnetic and antiferromagnetic chains have the same classical Helmholtz free energy. We show how this two types of media react to the presence of an external magnetic field.

cond-mat.stat-mech↗

arXiv2005

High-temperature series expansion of the Helmholtz free energy of the quantum spin-S XYZ chain

We consider the $XYZ$ chain model of arbitrary spin $S$ in the high temperature region, with external magnetic field and single-ion anisotropy term. Our high-temperature expansion of the Helmholtz free energy is analytic in the parameters of the model for $S$, which may range from 1/2 to the classical limit of infinite spin ($S\to \infty$). Our expansion is carried out up to order $(J β)^5$. Our results agree with numerical results of the specific heat per site for $S=1/2$, obtained by the Bethe ansatz, with $h=0$ and D=0. Finally, we show that the magnetic susceptibility and magnetization of the quantum model can be well approximated by their classical analog in this region of temperature.

cond-mat.stat-mech↗

arXiv2005

Thermodynamics of the quantum spin-S XXZ chain

The thermodynamics of the spin-$S$ anisotropic quantum $XXZ$ chain with arbitrary value of $S$ and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the $z$-direction are taken into account. We obtain, for arbitrary value of $S$, the $β$-expansion of the Helmholtz free energy of the model up to order $β^6$ and show that it actually depends on $\frac{1}{S(S+1)}$. Its classical limit is obtained by simply taking $S\to \infty$. At $h=0$ and D=0, our high temperature expansion of the classical model coincides with Joyce's exact solution\cite{joyce_prl}. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of $S$ those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin.

cond-mat.str-el↗

arXiv2005

Thermodynamics of the S=1 spin ladder as a composite S=2 chain model

A special class of S=1 spin ladder hamiltonians, with second- neighbor exchange interactions and with anisotropies in the $z$-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin $S_{eff}$, such that $S_{eff}(1+S_{eff})=< \vec{\bf S}_i^2>$, where ${\bf S}_i$ refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian.

cond-mat.str-el↗

arXiv2003

Phase diagram of a coupled tetrahedral Heisenberg model

The phase diagram of a coupled tetrahedral Heisenberg model is obtained. The quantum chain has a local gauge symmetry and its eigenspectrum is obtained by the composition of the eigenspectra of spin-1/2 XXZ chains with arbitrary distribution of spin-3/2 impurities. The phase diagram is quite rich with an infinite number of phases with ferromagnetic, antiferromagnetic or ferrimagnetic order. In some cases the ground state and the low lying eigenlevels of the model can be exactly calculated since they coincide with the eigenlevels of the exactly integrable XXZ chain. The thermodynamical properties of the model at low temperatures is also studied through finite-size analysis.

cond-mat.stat-mech↗