arXiv subjects

H. Chamati

Publications and source records attributed to H. Chamati.

At least 19 recordsLinked to original sources

arXiv2022

Control of a qubit state by a soliton propagating through a Heisenberg spin chain

We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a Hamiltonian involving the interaction between the soliton and the qubit. We show that under certain conditions the generic Hamiltonian may be mapped on that of a qubit two-level system with matrix elements depending on the soliton parameters. We considered the action of a bright and a dark solitons depending on the driving nonlinear wave function. We considered a local interaction restricted the closest to the qubit spin in the chain. We computed the expressions of the physical quantities of interest for all cases and analyzed their behavior in some special limits.

quant-ph↗

arXiv2022

Magnetostructural Dependencies in $3d^2$ Systems: The Trigonal Bipyramidal V$^{3+}$ Complex

We introduce a multi-configurational approach to study the magneto-structural correlations in $3d^2$ systems. The theoretical framework represents a restricted active space self-consistent field method, with active space optimized to the number of all non-bonding orbitals. To demonstrate the validity and effectiveness of the method, we explore the physical properties of the trigonal bipyramidal spin-one single-ion magnet (C$_6$F$_5$)$_3$trenVCN$^t$Bu. The obtained theoretical results show a good agreement with the experimental data available in the literature. This includes measurements for the magnetization, low-field susceptibility, cw-EPR and photoluminescence spectroscopy. The proposed method may be reliably applied to a variety of $3d^2$ magnetic systems. To this end, and for the sake completeness, we provide detailed analytical and numerical representations for the generic Hamiltonian's effective matrix elements related to the crystal field, exchange, spin-orbit and Zeeman interactions.

cond-mat.str-el↗

arXiv2022

Molecular magnetism in the multi-configurational self-consistent field method

We develop a structured theoretical framework used in our recent articles [Eur. Phys. J. B 92, 93 (2019) and Phys. Rev. B 101, 094427 (2020)] to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic susceptibility of the molecular magnet Ni$_4$Mo$_{12}$. The theoretical background is based on the molecular orbital theory in conjunction with the multi-configurational self-consistent field method and results in a post-Hartree-Fock scheme for constructing the corresponding energy spectrum. Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete coupling parameters accounting for the relevant spectroscopic magnetic excitations, magnetization and magnetic susceptibility. The explicit expressions of the eigenenergies of the ensuing Hamiltonian are determined and the physical origin of broadening and splitting of experimentally observed peaks in the magnetic spectra is discussed. To demonstrate the efficiency of our method we compute the spectral properties of a spin-one magnetic dimer. The present approach may be applied to a variety of magnetic units based on transition metals and rare earth elements.

cond-mat.str-el↗

arXiv2020

Dynamics of a periodic $XY$ chain coupled to a photon mode

We study the real-time dynamics of a periodic $XY$ system exposed to a composite field comprised of a constant homogeneous magnetic and a quantized circularly polarized electromagnetic fields. The interaction between the quantized mode and spin-magnetic moments is modeled by the Dicke Hamiltonian. The rotating wave approximation is applied and the conditions for its validity are discussed. It is shown that if initially all of the excitations are contained in the field, then in the regime of large detuning, the main evolutionary effect involves oscillations of the excitations between the zero-momentum modes of the chain and the field. Accordingly, the reduced photon number and magnetization per site reveal a sort of oscillatory behavior. Effective Hamiltonians describing the short-time dynamics of the present model for small number of excitations and large detuning are introduced. The resonance case is considered in the context of photon emission from the chain initially prepared in the (partially) excited state. In particular, it is demonstrated, in the framework of a specific example, that the superradiant behavior shows up at the beginning of the emission, when we have an initial state with a maximally excited $XY$ chain. Possible applications of the model to problems such as spin chain and $J$-aggregate in a single-mode cavity are discussed.

cond-mat.mes-hall↗

arXiv2020

Magnetization steps in the molecular magnet Ni$_4$Mo$_{12}$ revealed by complex exchange bridges

We study the behavior of the magnetization and the magnetic susceptibility of molecular magnets with complex bridging structure. Our computations are based on a post-Hartree-Fock method accounting for the intricate network of interatomic bonds and an effective spin-like Hamiltonian that captures the essential magnetic features of magnetic molecules. The devised method and the constructed Hamiltonian are further employed to characterize the magnetic properties of the molecular magnet Ni$_4$Mo$_{12}$. The obtained results reproduce both quantitatively and qualitatively the main features of the magnetic spectrum. Furthermore, the computations for the magnetization and the low-field susceptibility are in very good agreement with their experimental counterparts. In this respect, they improve upon the results obtained with conventional Heisenberg models.

cond-mat.str-el↗

arXiv2019

Magnetic excitations in molecular magnets with complex bridges: The tetrahedral molecule Ni$_4$Mo$_{12}$

We investigate the spectroscopic magnetic excitations in molecular magnets with complex intermediate structure among the magnetic ions. Our approach consists in introducing a modified spin Hamiltonian that allows for discrete coupling parameters accounting for all energetically favorable spatial distributions of the valence electrons along the exchange bridges connecting the constituent magnetic ions. We discuss the physical relevance of the constructed Hamiltonian and derive its eigenvalues. The model is applied to explore the magnetic excitations of the tetrameric molecular magnet Ni$_4$Mo$_{12}$. Our results are in a very good agreement with the available experimental data. We show that the experimental magnetic excitations in the named tetramer can be traced back to the specific geometry and complex chemical structure of the exchange bridges leading to the splitting and broadness of the peaks centered about 0.5 meV and 1.7 meV.

cond-mat.str-el↗

arXiv2019

Magnetic excitations in the trimeric compounds A$_3$Cu$_3$(PO$_4$)$_4$ (A = Ca, Sr, Pb)

We study the magnetic excitations of the trimeric magnetic compounds A$_3$Cu$_3$(PO$_4$)$_4$ (A = Ca, Sr, Pb). The spectra are analyzed in terms of the Heisenberg model and a generic spin Hamiltonian that accounts for the changes in valence electrons distribution along the bonds among magnetic ions. The analytical results obtained in the framework of both Hamiltonians are compared to each other and to the available experimental measurements. The results based on our model show better agreement with the experimental data than those obtained with the aid of the Heisenberg model. For all trimers, our analysis reveals the existence of one thin energy band referring to the flatness of observed excitation peaks.

physics.atm-clus↗

arXiv2018

Magnetic Exchange in Spin Clusters

We investigate the role of exchange bridges in molecular magnets. We explore their effects on the distribution of the valence electrons and their contribution to the exchange processes. The present study is focused on a spin-half dimer with nonequivalent exchange bridges. Here, we derive an effective Hamiltonian that allows for an accurate estimation of the observables associated to the magnetic properties of the magnet. Our results are compared to those obtained by means of the conventional Heisenberg model that usually fails.

physics.atm-clus↗

arXiv2018

A systematic approach to determine the spectral characteristics of molecular magnets

We devise a formalism to investigate in a systematic way the spectroscopic magnetic excitations in molecular magnets. This consists in introducing a bilinear spin Hamiltonian that allows for discrete coupling parameters accounting for distinct spin coupling mechanisms among the constituent magnetic ions, as well as the influence of the nonmagnetic ions in the system. The model is applied to explore the magnetic excitations of the trimeric magnetic compounds $\mathrm{A_3Cu_3(PO_4)_4}$ $\mathrm{(A\ =\ Ca,\ Sr,\ Pb)}$ and the tetrameric molecular magnet $\mathrm{Ni_4Mo_{12}}$. Our results are in a very good agreement with the available experimental data: For all trimers $\mathrm{A_3Cu_3(PO_4)_4}$, calculations reveal the existence of one thin energy band referring to the flatness of observed excitation peaks. Moreover for the tetramer $\mathrm{Ni_4Mo_{12}}$, we concluded that the magnetic excitations may be traced back to the specific geometry and complex chemical structure of the exchange bridges leading to the splitting and broadness of the peaks centered about 0.5 meV and 1.7 meV.

cond-mat.str-el↗

arXiv2016

Energy spectra of a spin-$\tfrac12$ XY spin molecule interacting with a single mode field cavity: Numerical study

In a previous paper [J. Phys.: Conf. Ser. 682 (2016) 012032}, arXiv:1605.05593] we studied analytically the energy spectra of a finite-size spin $\tfrac12$ XY chain (molecule) coupled at an arbitrary spin site to a single mode of an electromagnetic field via the Jaynes-Cummings model. We considered spin rings and open spin molecules with up to 4 spins and an interaction restricted to nearest-neighbours. Here we extend our investigation, addressing numerically the energy spectra of molecules of up to 10 spins with nearest-neighbour or long-range interaction. Furthermore we analyze the behaviour of an invariant operator, constructed by combining the magnetization of the spin-chain and the total number of photons in the system. We found a strong dependence on the number (even or odd) of sites in the molecules. This study is aimed at finding the appropriate combination of the physical parameters that could make the system suitable for use in quantum computations.

quant-ph↗

arXiv2016

Interaction of a single mode field cavity with the 1D XY model: Energy spectrum

In this work we use the fundamental in quantum optics Jaynes-Cummings model to study the response of spin $\tfrac12$ chain to a single mode of a laser light falling on one of the spins, a focused interaction model between the light and the spin chain. For the spin-spin interaction along the chain we use the XY model. We report here the exact analytical results, obtained with the help of a computer algebra system, for the energy spectrum in this model for chains of up to 4 spins with nearest neighbors interactions, either for open or cyclic chain configurations. Varying the sign and magnitude of the spin exchange coupling relative to the light-spin interaction we have investigated both cases of ferromagnetic or antiferromagnetic spin chains.

quant-ph↗

arXiv2014

Nematic order by thermal disorder in a three-dimensional lattice-spin model with dipolar-like interactions

At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example nearest-neighbour interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second--rank) order, in addition to the primary first-rank one; on the other hand, in the Literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with Finite-Size Scaling analysis have been used for characterizing its critical behaviour; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.

cond-mat.stat-mech↗

arXiv2012

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the ${\cal O}(n)$ vector $ϕ^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-σ}$, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature $T_c$. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. $0<σ<2$ and it turns out to be exponential in case of short-range interaction i.e. $σ=2$. The results are valid for arbitrary dimension $d$, between the lower ($d_<=σ$) and the upper ($d_>=2σ$) critical dimensions.

cond-mat.stat-mech↗

arXiv2011

Dynamic critical phenomena in disordered systems with finite geometry

We study the critical dynamics of hyper-cubic finite size system in the presence of quenched short-range correlated disorder. By using the random $T_c$ model A for the critical dynamics and the renormalization group method in the vicinity of the upper critical dimension $d=4$, we derive in first order of $ε$ the expression for the relaxation time. Its finite-size scaling behavior is discussed both analytically and numerically in details. This was made possible by analyzing carefully the finite--size effects on the Onsager kinetic coefficient. The obtained results are compared to those reported in the literature.

cond-mat.dis-nn↗

arXiv2011

Quantum critical scaling and the Gross-Neveu model in 2+1 dimensions

The quantum critical behavior of the 2+1 dimensional Gross--Neveu model in the vicinity of its zero temperature critical point is considered. The model is known to be renormalisable in the large $N$ limit, which offers the possibility to obtain expressions for various thermodynamic functions in closed form. We have used the concept of finite--size scaling to extract information about the leading temperature behavior of the free energy and the mass term, defined by the fermionic condensate and determined the crossover lines in the coupling ($\g$) -- temperature ($T$) plane. These are given by $T\sim|\g-\g_c|$, where $\g_c$ denotes the critical coupling at zero temperature. According to our analysis no spontaneous symmetry breaking survives at finite temperature. We have found that the leading temperature behavior of the fermionic condensate is proportional to the temperature with the critical amplitude $\frac{\sqrt{5}}3π$. The scaling function of the singular part of the free energy is found to exhibit a maximum at $\frac{\ln2}{2π}$ corresponding to one of the crossover lines. The critical amplitude of the singular part of the free energy is given by the universal number $\frac13[\frac1{2π}ζ(3)-\mathrm{Cl}_2(\fracπ3)]=-0.274543...$, where $ζ(z)$ and $\mathrm{Cl}_2(z)$ are the Riemann zeta and Clausen's functions, respectively. Interpreted in terms the thermodynamic Casimir effect, this result implies an attractive Casimir "force". This study is expected to be useful in shedding light on a broader class of four fermionic models.

cond-mat.str-el↗

arXiv2009

Comment on "Quantum critical paraelectrics and the Casimir effect in time"

At variance with the authors' statement [L. Pálová, P. Chandra and P. Coleman, Phys. Rev. B 79, 075101 (2009)], we show that the behavior of the universal scaling amplitude of the gap function in the phonon dispersion relation as a function of the dimensionality $d$, obtained within a self--consistent one--loop approach, is consistent with some previous analytical results obtained in the framework of the $ε$--expansion in conjunction with the field theoretic renormalization group method [S. Sachdev, Phys. Rev. B 55, 142 (1997)] and the exact calculations corresponding to the spherical limit i.e. infinite number $N$ of the components of the order parameter [H. Chamati. and N. S. Tonchev, J. Phys. A: Math. Gen. 33, 873 (2000)]. Furthermore we determine numerically the behavior of the "temporal" Casimir amplitude as a function of the dimensionality $d$ between the lower and upper critical dimension and found a maximum at $d=2.9144$. This is confirmed via an expansion near the upper dimension $d=3$.

cond-mat.stat-mech↗

arXiv2009

Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions

The critical dynamics of relaxational stochastic models with nonconserved $n$-component order parameter $\bmϕ$ and no coupling to other slow variables ("model A") is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian $\mathcal{H}$ governing the stationary equilibrium distribution is taken to be O(n) symmetric and to involve, in the case of free boundary conditions, the boundary terms $\int_{\mathfrak{B}_j}\mathring{c}_j ϕ^2/2$ associated with the two confining surface planes $\mathfrak{B}_j$, $j=1,2$, at $z=0$ and $z=L$, where the enhancement variables $\mathring{c}_j$ are presumed to be subcritical or critical. A field-theoretic RG study of the dynamic critical behavior at $d=4-ε$ bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at $T_{c,\infty}$. This applies when either both $\mathring{c}_j$ take the critical value $\mathring{c}_{\text{sp}}$ associated with the special surface transition, or else periodic boundary conditions are imposed. Owing to the zero modes, the $ε$ expansion becomes ill-defined at $T_{c,\infty}$. Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-$ε$ expansion involving half-integer powers of $ε$, modulated by powers of $\lnε$. Explicit results for the scaling functions of $T$-dependent finite-size susceptibilities at temperatures $T\ge T_{c,\infty}$ and of layer and surface susceptibilities at the bulk critical point are given to orders $ε$ and $ε^{3/2}$, respectively. For the case of periodic boundary conditions, the consistency of the expansions to $O(ε^{3/2})$ with exact large-$n$ results is shown.

cond-mat.stat-mech↗

arXiv2008

Finite-size effects in the spherical model of finite thickness

A detailed analysis of the finite-size effects on the bulk critical behaviour of the $d$-dimensional mean spherical model confined to a film geometry with finite thickness $L$ is reported. Along the finite direction different kinds of boundary conditions are applied: periodic $(p)$, antiperiodic $(a)$ and free surfaces with Dirichlet $(D)$, Neumann $(N)$ and a combination of Neumann and Dirichlet $(ND)$ on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary $d$. It is found, for $2<d<4$, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for $(p)$ and $(a)$. For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At $d=3$, the critical amplitude of the singular part of the free energy (related to the so called Casimir amplitude) is estimated. We obtain $Δ^{(p)}=-2ζ(3)/(5π)=-0.153051...$, $Δ^{(a)}=0.274543...$ and $Δ^{(ND)}=0.01922...$, implying a fluctuation--induced attraction between the surfaces for $(p)$ and repulsion in the other two cases. For $(D)$ and $(N)$ we find a logarithmic dependence on $L$.

cond-mat.stat-mech↗