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M. T. Thomaz

Publications and source records attributed to M. T. Thomaz.

At least 19 recordsLinked to original sources
arXiv2015

The $β$-expansion of the $D=1$ fermionic spinless Hubbard model off the half-filling regime

We found that when the spinless model is off the half-filling regime ($μ\neq V$), the Helmholtz free energy (HFE) can be written as two $β$-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter $x = μ- V$. We show numerically that the chemical potential as a function of temperature satisfies a relation similar to the one derived from the particle-hole symmetry of the fermionic spinless model. We extend the $β$-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order $β^8$.

cond-mat.str-el↗
arXiv2015

Comparison of the ferromagnetic Blume-Emery-Griffiths model and the AF spin-1 longitudinal Ising model at low temperature

We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the $z$-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at $T=0$, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in[S.M. de Souza and M.T. Thomaz, J. of Mag. and Mag. Mat. {354} (2014) 205]. We explore the implications of the equality of phase diagrams, at $T=0$, of the ferromagnetic BEG model with $\frac{K}{|J|} = -2$ and of the spin-1 AF Ising model for $\frac{D}{|J|} > \frac{1}{2}$.

cond-mat.stat-mech↗
arXiv2014

On the particle-hole symmetry of the fermionic spinless Hubbard model in $D=1$

We revisit the particle-hole symmetry of the one-dimensional ($D=1$) fermionic spinless Hubbard model, associating that symmetry to the invariance of the Helmholtz free energy of the one-dimensional spin-1/2 $XXZ$ Heisenberg model, under reversal of the longitudinal magnetic field and at any finite temperature. Upon comparing two regimes of that chain model so that the number of particles in one regime equals the number of holes in the other, one finds that, in general, their thermodynamics is similar, but not identical: both models share the specific heat and entropy functions, but not the internal energy per site, the first-neighbor correlation functions, and the number of particles per site. Due to that symmetry, the difference between the first-neighbor correlation functions is proportional to the $z$-component of magnetization of the $XXZ$ Heisenberg model. The results presented in this paper are valid for any value of the interaction strength parameter $V$, which describes the attractive/null/repulsive interaction of neighboring fermions.

cond-mat.stat-mech↗
arXiv2013

The magnetization plateaus of the ferro and anti-ferro spin-1 classical models with $S_z^2$ term

We study in detail the exact thermodynamics of the one-dimensional standard and staggered spin-1 Ising models with a single-ion anisotropy term in the presence of a longitudinal magnetic field at low temperatures. The results are valid for the ferromagnetic and anti-ferromagnetic (AF) models and for positive and negative values of the crystal field for $T>0$. Although the excited states of the ferro and anti-ferro models are highly degenerate, we show that the temperature required for reaching the first excited state in the classical spin-1 ferro model gives a scale of temperature that permits fitting the z-component of the magnetization only by the contribution of two ground states of the model. This approximation is not true for the equivalent AF function due to the fact that the AF model is gapless along the lines separating the phases in its phase diagram at T=0. We relate the number of plateaus in the magnetization of each model to their respective phase diagrams at T=0. The specific heat per site of the AF model distinguishes, at low temperature, the transitions $\mbox{A} \rightleftharpoons \mbox{E}$ and $\mbox{G} \rightleftharpoons \mbox{E}$ as the external magnetic field is varied. The exact Helmholtz free energy of the classical spin-1 model is mapped onto the equivalent function of the ionic limit of the 1D extended Hubbard model by proper transformations.

cond-mat.stat-mech↗
arXiv2012

The high-temperature expansion of the classical Ising model with S_z^2 term

We derive the high-temperature expansion of the Helmholtz free energy up to the order β^{17} of the one-dimensional spin-S Ising model, with single-ion anisotropy term, in the presence of a longitudinal magnetic field. We show that the values of some thermodynamical functions for the ferromagnetic models, in the presence of a weak magnetic field, are not small corrections to their values with h=0. This model with S=3 was applied by Kishine et al. [J.-i. Kishine et al., Phys. Rev. B, 2006, 74, 224419] to analyze experimental data of the single-chain magnet [Mn (saltmen)]_2 [Ni(pac)_2 (py)_2] (PF_6)_2 for T<40 K. We show that for T<35 K the thermodynamic functions of the large-spin limit model are poor approximations to their analogous spin-3 functions.

cond-mat.stat-mech↗
arXiv2010

Phases of the electronic two-level model under the rotating wave approximation

We present the time evolution of the electronic two-level model in the rotating wave approximation (RWA). We calculate the Aharonov-Anandan phase of the vector states with cyclic evolution either within the period of an external monochromatic electric field or the period corresponding to Rabi's frequency. The Aharonov-Anandan phase is shown to be dependent on the initial vector state, unless the system evolves in the adiabatic regime; in the latter case, the Aharonov-Anandan phase recovers Berry's phase. Our results are also discussed in the quasi-resonant regime.

quant-ph↗
arXiv2009

Contribution of adiabatic phases to noncyclic evolution

We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of non-degenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical quantities in states that are a superposition of instantaneous eigenstates of energy. To verify the contribution of those adiabatic phases in the interference phenomena, we consider the spin-1/2 model coupled to a precessing external magnetic field. In the model, the adiabatic phase increases in time up to reach the difference of the Berry's phases of the model when the external magnetic field completes a period.

quant-ph↗
arXiv2009

Berry's phase in the two-level model

We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation. In this regime, we show the absence of geometric phases in the interacting two-level model in the presence of any periodic real time-dependent classical electric field. We obtain a conservative scalar potential in the calculation of Berry's phases of the instantaneous eigenstates of the model. For complex electric fields, we recover the existence of geometric phases. In particular, the geometric phases of the instantaneous eigenstates of the model in the presence of a positive or of a negative frequency component of the monochromatic electric field differ by an overall sign. As a check on our results, we map this interacting two-level model onto a spin-1/2 model under the action of a classical magnetic field. We confirm that the first one acquires Berry's phase only in the rotating wave approximation [RWA].

quant-ph↗
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

Imaginary Phases in Two-Level Model with Spontaneous Decay

We study a two-level model coupled to the electromagnetic vacuum and to an external classic electric field with fixed frequency. The amplitude of the external electric field is supposed to vary very slow in time. Garrison and Wright [{\it Phys. Lett.} {\bf A128} (1988) 177] used the non-hermitian Hamiltonian approach to study the adiabatic limit of this model and obtained that the probability of this two-level system to be in its upper level has an imaginary geometric phase. Using the master equation for describing the time evolution of the two-level system we obtain that the imaginary phase due to dissipative effects is time dependent, in opposition to Garrison and Wright result. The present results show that the non-hermitian hamiltonian method should not be used to discuss the nature of the imaginary phases in open systems.

quant-ph↗
arXiv2002

Thermodynamics of the one-dimensional s=1 XXZ Heisenberg model: analytical results

We apply the results recently derived by Rojas et al. to derive the beta-expansion of the Helmholtz free energy of the spin-1 XXZ Heisenberg model up to 5th order in beta. The analytical expansion obtained is valid for all phases of this model. Our curves of the specific heat fit well Bloete's numerical results in the high temperature regime.

cond-mat↗
arXiv2002

A Comment on the beta-expansion of s=1/2 and s=1 Ising Models

The purpose of the present work is to apply the method recently developed in reference [chain_m] to the spin-1 Ising chain, showing how to obtain analytical $β$-expansions of thermodynamical functions through this formalism. In this method, we do not solve any transfer matrix-like equations. A comparison between the $β$-expansions of the specific heat and the magnetic susceptibility for the $s=1/2$ and $s=1$ one-dimensional Ising models is presented. We show that those expansions have poorer convergence when the auxiliary function of the model has singularities.

cond-mat↗
arXiv2002

Berry's Phase in the Presence of a Dissipative Medium

We consider the spin 1/2 model coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operators. We show that Berry's geometrical phase remains unaltered by the two dissipation mechanism considered. Dissipation effects are twofold: a shrinking in the modulus of the Bloch's vector, which characterizes coherence loss and a time dependent (dissipation related) precession angle. We show that the line broadening of the Fourier transformation of the components of magnetization is only due to the presence of dissipation.

quant-ph↗
arXiv2002

Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems

We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1/2 model coupled to reservoir at thermodynamic equilibrium.

quant-ph↗