arXiv subjects

Marie-Bernadette Lepetit

Publications and source records attributed to Marie-Bernadette Lepetit.

36 records · Page 2Linked to original sources

arXiv2005

How to determine model Hamiltonians for strongly correlated materials

The present paper reviews recent achievements on the ab initio determination of effective model Hamiltonians aimed at the description of strongly correlated materials. These models (Heisenberg, $t-J$, extended Hubbard, Kondo, etc) are crucial to solid state physicists for the description and understanding of the electronic remarkable properties such as magnetic orders, photo-induced magnetism, transport properties, high $t\_c$ super conductivity, etc. We will see how the association and the control of embedding techniques, fragment spectroscopy, effective or intermediate Hamiltonian theories, provides a systematic and well controlled method for the determination of trustworthy models Hamiltonians.

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arXiv2005

Charge order in the incommensurate compounds $Sr\_{14-x}Ca\_xCu\_{24}O\_{41}$

The present paper studies, using ab-initio calculations, the influence of the incommensurate structural modulations on the low energy physics of the $Sr\_{14-x}Ca\_xCu\_{24}O\_{41}$ oxides. On-site, nearest-neighbor and next-nearest-neighbor effective parameters were computed within a $t-J+V$ model based on the copper magnetic orbitals. The structural modulations appear to be the key degree of freedom, responsible for the low energy properties such as the electron localization, the formation of dimers in the $x=0$ compound or the anti-ferromagnetic order in the $x=13.6$ compound.

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arXiv2005

Leading interactions in the $β$-$Sr V_6 O_{15}$ compound

The present study shows that the electronic structure of the $β$-$AV\_6O\_{15}$ family of compounds ($A = Sr, Ca, Na ...$) is based on weakly interacting two-leg ladders, in contrast with the zig-zag chain model one could expect from their crystal structure. Spin dimer analysis, based on extended Hückel tight-binding calculations, was performed to determine the structure of the dominant transfer and magnetic interactions in the room temperature $β$-$SrV\_6O\_{15}$ phase. Two different two-legs ladders, associated with different charge/spin orders are proposed to describe these one-dimensional $β$-type systems. The antiferromagnetic ladders are packed in an 'IPN' geometry and coupled to each other through weak antiferromagnetic interactions. This arrangement of the dominant interactions explains the otherwise surprising similarities of the optical conductivity and Raman spectra for the one-dimensional $β$-type phases and the two-dimensional $α$-type ones such as the well-known $α^\prime$-$NaV\_2O\_5$ system.

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arXiv2004

Electronic structure of the $Sr_{0.4}Ca_{13.6}Cu_{24}O_{41}$ incommensurate compound

We extracted, from strongly-correlated ab-initio calculations, a complete model for the chain subsystem of the $Sr_{0.4}Ca_{13.6}Cu_{24}O_{41}$ incommensurate compound. A second neighbor $t-J+V$ model has been determined as a function of the fourth crystallographic parameter $τ$, for both low and room temperature crystallographic structures. The analysis of the obtained model shows the crucial importance of the structural modulations on the electronic structure through the on-site energies and the magnetic interactions. The structural distortions are characterized by their long range effect on the cited parameters that hinder the reliability of analyses such as BVS. One of the most striking results is the existence of antiferromagnetic nearest-neighbor interactions for metal-ligand-metal angles of $90^\circ$. A detailed analysis of the electron localization and spin arrangement is presented as a function of the chain to ladder hole transfer and of the temperature. The obtained spin arrangement is in agreement with antiferromagnetic correlations in the chain direction at low temperature.

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arXiv2004

Influence of the incommensurability in $Sr_{14-x}Ca_xCu_{24}O_{41}$ family compounds

The present paper studies the influence of the structural modulation on the low energy physics of the $Sr_{14-x}Ca_xCu_{24}O_{41}$ oxides, using ab-initio determination of the on-site and nearest neighbor effective parameters. The structural modulations appears to be the key degree of freedom, responsible for the low energy properties, such as the electron localization, the formation of dimers in the $x=0$ compound or the anti-ferromagnetic order in the $x=13.6$ compound.

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arXiv2003

Magnetic ligands in the $Pt_2(dta)_4I$ compound

We report a reinterpretation of the electronic structure of the $(Pt)_2I(dta)_4$ compound, based on {\em ab initio} embedded fragment calculations. Our major results are the following. First, the usually assumed electronic intra-dimer charge ordering is unrealistic. Second, the $(dta)$ ligands take part actively in the magnetic properties of the system. The proposed electronic structure is favorably confronted to experimental data. In particular, the unexplained $3:1$ $Pt^{2+}/Pt^{3+}$ abundances ratio of the XPS spectra is rationalized.

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arXiv2003

Environment effects on effective magnetic exchange integrals and local spectroscopy of extended strongly correlated systems

The present work analyzes the importance of the different components of the environment effects on the local spectroscopy of extended strongly correlated systems. It has been found that the usual formal charge definition of the charge transfer and Madelung potential are far too crude for an accurate determination of the local excitation energies in embedded fragment calculations. A criterion for the validation of the embedding against the infinite system density of states has been proposed.

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arXiv2003

The role of dynamical polarization of the ligand to metal charge transfer excitations in {\em ab initio} determination of effective exchange parameters

The role of the bridging ligand on the effective Heisenberg coupling parameters is analyzed in detail. This analysis strongly suggests that the ligand-to-metal charge transfer excitations are responsible for a large part of the final value of the magnetic coupling constant. This permits to suggest a new variant of the Difference Dedicated Configuration Interaction (DDCI) method, presently one of the most accurate and reliable for the evaluation of magnetic effective interactions. This new method treats the bridging ligand orbitals mediating the interaction at the same level than the magnetic orbitals and preserves the high quality of the DDCI results while being much less computationally demanding. The numerical accuracy of the new approach is illustrated on various systems with one or two magnetic electrons per magnetic center. The fact that accurate results can be obtained using a rather reduced configuration interaction space opens the possibility to study more complex systems with many magnetic centers and/or many electrons per center.

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arXiv2002

Current-current correlations in a CuO_3 model system

We study a 3-band extended Hubbard model on a CuO_3 system by the density matrix renormalization group (DMRG) method. Our system has geometry similar to that of a section of the CuO_2 plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbour repulsions on the current-current correlations of two model CuO_3 systems. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show that repulsive interactions are capable of enhancing correlations involving at least one copper-oxygen rung over distances comparable to the length of the system. In some cases, V decreases the exponent corresponding to the power-law decay, leading to a considerable slowing down of the long-distance decay of the current-current correlations, compared to that of the Hubbard model.

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arXiv2002

Similarities between the $t-J$ and Hubbard models in weakly correlated regimes

We present a comparative study of the Hubbard and $t-J$ models far away from half-filling. We show that, at such fillings the $t-J$ Hamiltonian can be seen as an effective model of the repulsive Hubbard Hamiltonian over the whole range of correlation strength. Indeed, the $|t/U| \in [0,+\infty [$ range of the Hubbard model can be mapped onto the finite range $|J/t| \in [1, 0 ]$ of the $t-J$ model, provided that the effective exchange parameter $J$ is defined variationally as the local singlet-triplet excitation energy. In this picture the uncorrelated limit U=0 is associated with the super-symmetric point $J=-2|t|$ and the infinitely correlated $U=+\infty$ limit with the usual J=0 limit. A numerical comparison between the two models is presented using different macroscopic and microscopic properties such as energies, charge gaps and bond orders on a quarter-filled infinite chain. The usage of the $t-J$ Hamiltonian in low-filled systems can therefore be a good alternative to the Hubbard model in large time-consuming calculations.

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arXiv2002

Effect of nearest neighbor repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain

We have studied the influence of nearest-neighbor (NN) repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain. The NN repulsion term induces the apparition of two new long range ordered phases (one $4k_F$ CDW for positive $U_{eff} = U-2g^2/ω$ and one $2k_F$ CDW for negative $U_{eff}$) that did not exist in the V=0 phase diagram. These results are put into perspective with the newly observed charge ordered phases in organic conductors and an interpretation of their origin in terms of electron-molecular vibration coupling is suggested.

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arXiv2001

Ab initio evaluation of the charge-ordering in $α^\prime NaV_2O_5$

We report {\it ab initio} calculations of the charge ordering in $α^\prime NaV_2O_5$ using large configurations interaction methods on embedded fragments. Our major result is that the $2p_y$ electrons of the bridging oxygen of the rungs present a very strong magnetic character and should thus be explicitly considered in any relevant effective model. The most striking consequence of this result is that the spin and charge ordering differ substantially, as differ the experimental results depending on whether they are sensitive to the spin or charge density.

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arXiv2001

Fractionnally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k$_F$ charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological unbound solitons carrying charge $e/2$. Relevance to the 4k$_F$ charge density wave instability in $\rm (DI-DCNQI)_2Ag$ or recently discovered in (TMTTF)$_2$X (X=PF$_6$, AsF$_6$) is discussed.

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arXiv2000

Optical phonons in a quarter-filled 1D Hubbard model

The influence of dispersion-less quantum optical phonons on the phase diagram of a quarter-filled Hubbard chain is studied using the Density-matrix renormalization group technique. The ground state phase diagram is obtained for frequencies corresponding to the intra-molecular vibrations in organic conductors. For high vibrational modes the system is only slightly affected by the electron-phonons coupling. It remains in a Lüttinger liquid phase as long as the electronic repulsion is larger than the polaronic binding energy. For low vibrational modes the phase diagram is very rich. A noticeable point is the existence of a $4k_F$ CDW phase for small values of the correlation strength. For realistic values of the electron repulsion and of the electron-phonons coupling constant a large phonons-mediated reduction of the Lüttinger liquid parameter $K_ρ$ was found compared to the pure electronic model.

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arXiv2000

Ab initio evaluation of local effective interactions in $α^\prime NaV_2O_5$

We will present the numerical evaluation of the hopping and magnetic exchange integrals for a nearest-neighbor $t-J$ model of the quarter-filled $α^\prime NaV_2O_5$ compound. The effective integrals are obtained from valence-spectroscopy {\em ab initio} calculations of embedded crystal fragments (two $VO_5$ pyramids in the different geometries corresponding to the desired parameters). We are using a large configurations interaction (CI) method, where the CI space is specifically optimized to obtain accurate energy differences. We show that the $α^\prime NaV_2O_5$ system can be seen as a two-dimensional asymmetric triangular Heisenberg lattice where the effective sites represent delocalized $V-O-V$ rung entities supporting the magnetic electrons.

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arXiv1998

Correlation and Dimerization Effects on the Physical Behavior of the $NR_4 [Ni(dmit)_2]_2$ Charge Transfer Salts : A DMRG Study of the Quarter-Filling t-J Model

The present work studies the quasi one-dimensional $Ni(dmit)_2$-based compounds within a correlated model. More specifically, we focus our attention on the composed influence of the electronic dimerization-factor and the repulsion, on the transport properties and the localization of the electronic density in the ground-state. Those properties are studied through the computation of the charge gaps (difference between the ionization potential and the electro-affinity: IP-EA) and the long- and short-bond orders of an infinite quarter-filled chain within a $t-J(t,U)$ model. The comparison between the computed gaps and the experimental activation energy of the semiconductor $NH_2Me_2 [Ni(dmit)_2]_2$ allows us to estimate the on-site electronic repulsion of the $Ni(dmit)_2$ molecule to $1.16eV$.

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arXiv1998

Density-matrix renormalization using three classes of block states

An extension of the the density matrix renormalization group (DMRG) method is presented. Besides the two groups or classes of block states considered in White's formulation, the retained $m$ states and the neglected ones, we introduce an intermediate group of block states having the following $p$ largest eigenvalues $λ_i$ of the reduced density matrix: $λ_1 \ge >... λ_m \ge λ_{m+1}\ge ... \ge λ_{m+p}$. These states are taken into account when they contribute to intrablock transitions but are neglected when they participate in more delocalized interblock fluctuations. Applications to one-dimensional models (Heisenberg, Hubbard and dimerized tight-binding) show that in this way the involved computer resources can be reduced without significant loss of accuracy. The efficiency and accuracy of the method is analyzed by varying $m$ and $p$ and by comparison with standard DMRG calculations. A Hamiltonian-independent scheme for choosing $m$ and $p$ and for extrapolating to the limit where $m$ and $p$ are infinite is provided. Finally, an extension of the 3-classes approach is outlined, which incorporates the fluctuations between the $p$ states of different blocks as a self-consistent dressing of the block interactions among the retained $m$ states.

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arXiv1998

Density-matrix renormalization study of the Hubbard model on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number $z=3$ is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy $E$, average local magnetization $<\hat S_z>$, its fluctuations $<\hat S_z^2 > - < \hat S_z>^2$ and various spin correlation functions $<\hat S_z(i) \hat S_z(j) > - < S_z(i)> < S_z(j)>$ are determined as a function of the Coulomb interaction strength $U/t$. The calculated local magnetic moments $<\hat S_z(i)>$ increase monotonically with increasing Coulomb repulsion $U/t$ forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large $U/t$, $<\hat S_z(i)>$ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins ($|< S_z(i)>|\simeq 0.35$ for $U/t\to +\infty$). $ - < S_z(i)>^2$ shows a maximum for $U/t=2.4$--2.9 which results from the interplay between the usual increase of $ $ with increasing $U/t$ and the formation of important permanent moments $ $ at large $U/t$. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of $U/t$. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.

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