Theoretical study of the optical conductivity of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">NaV</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn>

Cuoco, Mario; Horsch, Peter; Mack, Frank

doi:10.1103/physrevb.60.r8438

Cited by 28 publications

(46 citation statements)

References 27 publications

(37 reference statements)

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“…In this large-U limit the extended Hubbard model reduces to a socalled t-J-V model which can explain insulating properties and optical spectra of NaV 2 O 5 . 24 Our calculations do show a formation of the lower and upper Hubbard bands which leads to the spectral density transfer and moves the Fermi energy into the pseudogap between bonding and anti-bonding states in the lower Hubbard band as it was proposed qualitatively in Refs. 5 and 6.…”

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Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

et al. 2002

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The nature of the insulating state driven by electronic correlations in the quarter-filled ladder compound ␣ЈNaV 2 O 5 is investigated within a cluster dynamical mean-field approach. An extended Hubbard model with first-principles tight-binding parameters has been used. It is shown that the insulating state in the chargedisordered phase of this compound is formed due to the transfer of spectral density and dynamical charge fluctuations where for the latter, the role of intersite Coulomb interaction is found to be of crucial importance. (V 4.5ϩ ), whereas below T c , a charge disproportionation appears. Analysis of the additional experimental data on the microwave dielectric susceptibility, entropy change at T c , and magnetic-field effect on T c has led to an unambigious conclusion about zigzag charge ordering ͑for a review, see Ref. 9͒.Both the charge-ordered phase and charge-disordered one are insulating with an energy gap of the order of 0.8-1 eV. 3The presence of the gap in the ordered phase is not surprising and it was reproduced successfully, for example, in the recent local-density approximation ͑LDA͒ϩU calculations. 11The properties of the disordered phase are much more difficult to understand. In contrast to the isostructural ladder compound CaV 2 O 5 , NaV 2 O 5 has a quarter-filled band 2 rather than a half-filled one and cannot be considered as a standard Mott insulator. It has been proposed in Refs. 5 and 6 that a large value of the transverse hopping parameter in the ladder which splits the band into sub-bands of the bonding and antibonding states 2 could be responsible for the Mott insulator behavior in NaV 2 O 5 in the presence of strong Coulomb interactions. However, it is not known whether this mechanism is adequate for the realistic values of the parameters characterizing the single-particle electronic structure and the electron-electron correlations.In this paper we investigate the correlation effects in NaV 2 O 5 taking into account nonlocal dynamical charge fluctuations on the rung for this two-leg ladder compound. This allows us to understand the origin of the insulating state above T c and to estimate the relative importance of various physical mechanisms responsible for the gap formation.The crystal structure of NaV 2 O 5 projected in the xy plane is sketched in Fig. 1 Fig. 1͒. In this state one has approximately one d electron per rung of the vanadium ladder. We start with LDAϩU ͑Ref. 13͒ calculations of the ordered states but, in contrast to the previous work, 11 we considered several different types of the charge ordering. This gives us an opportunity to estimate the on-site and intersite Coulomb interactions U and V.It is natural to assume that the tendency to keep the number of d electrons per rung close to unity also takes place above the transition temperature leading to strong shortrange order and well-developed dynamical charge fluctuations. This is confirmed by the temperature dependencies of the spin gap and the entropy measurements.12 Usual LDA as well as the mean-field th...

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Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

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“…In NaV 2 O 5 the E a peak is around three times more intense than the E b peak. Thus, according to the t-J-V model [13], the hopping energy t b is expected to be at least two times smaller, t b ∼ 0.2 eV. From LiV 2 O 5 optical spectra we learned that major effect of charge localization involves peak intensities.…”

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“…The arguments are mostly based on the insensitivity of the phase-transition effects associated with magnetic fields. Subsequently, several theoretical analyses of the role of the electron correlations (intersite Coulomb interaction) in charge dynamics and/or charge ordering of NaV 2 O 5 were presented [10][11][12][13]. In these studies, the various charge-ordering ground states were proposed for the low-temperature phase of NaV 2 O 5 .…”

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“…We first focus on excitations around 1 eV in the NaV 2 O 5 spectra, and discuss the results in light of the electronic band structure of NaV 2 O 5 obtained from density-functional calculations, (DFC's) [25] and t-j-V model [10][11][12][13]. According to DFC's, the vanadium d-level degeneracy is removed due to anisotropy of the crystal field [25] and the lowest occupied 3d xy states are separated by 1-5 eV from remaining 3d states.…”

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Charge ordering and optical transitions ofLiV2O5and
Konstantinović
¹
,
Dong
²
,
Ziaei
³

et al. 2001
Phys. Rev. B
12
1
13
0
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We present measurements of the polarized optical spectra of NaV 2 O 5 and LiV 2 O 5 . In an energy range from 0.5 to 5.5 eV, we observe similar peaks in the E a spectra of NaV 2 O 5 and LiV 2 O 5 , which suggests similar electronic structures along the a axis in both materials. On the other hand, we find an almost complete suppression of the peaks in σ b of LiV 2 O 5 around 1 and 5 eV. We attribute this suppression to the charge localization effect originating from the existence of a double-chain charge-ordering pattern in LiV 2 O 5 . : 78.40.-q, 71.35.-y, 75.50.-y In the past several years, quantum phenomena resulting from the low dimensionality of effective electron interactions in solids have been investigated with increasing intensity from both experimental and theoretical points of view. The increase in interest was partially motivated by the discovery of inorganic materials which exhibit quantum effects, such as the PACS, and by a common belief that these studies would give us a better understanding of electron correlations in general.The vanadate family of AV 2 O 5 oxides have demonstrated a variety of the low-dimensional phenomena which originate from their peculiar crystal structures [3]. These oxides are quasi two-dimensional (2D) materials with layers formed by V O 5 square pyramids. The A atoms are situated between layers as intercalants, but in fact they determine the valence state of vanadium atoms (acting as charge reservoirs). If the A atoms belong to the first column in the periodic table, such as A = Li, Na, each valence electron is shared between two vanadium atoms. As a result the V ions are in a mixed valence-state with an average valence of +4.5. The common consequence of mixed valence in these structures is the appearance of a quasi-1D magnetic interaction, since chains carrying the spin (made of V 4+ , S=1/2) are separated from each other by nonmagnetic chains (V 5+ ). In both LiV 2 O 5 and NaV 2 O 5 the 1D character of the magnetic ordering was confirmed [4,5]. In addition, there is a possibility of the existence of strong valence fluctuations, and eventually charge ordering (CO) effects.

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“…The Finite Temperature Lanczos Method (FTLM), introduced by Jaklič and Prelovšek [1], has in recent years allowed the precise calculation of thermodynamic quantities of strongly correlated systems. It has been applied to the t-J model for the cuprates [2,3,4,5,6,7,8] and vanadates [9,10], orbital t-J model [11], Kondo lattice model [12], Heisenberg model [13] and static properties of the Hubbard model [14,15]. In principle this method can be applied at all temperatures, but at low temperatures the required number of random samples is very large.…”

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Low-temperature Lanczos method for strongly correlated systems

et al. 2003

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We present a modified finite temperature Lanczos method for the evaluation of dynamical and static quantities of strongly correlated electron systems that complements the finite temperature method (FTLM) introduced by Jaklič and Prelovšek for low temperatures. Together they allow accurate calculations at any temperature with moderate effort. As an example we calculate the static spin correlation function and the regular part of the optical conductivity σ reg (ω) of the one dimensional Hubbard model at half-filling and show in detail the connection between the ground state and finite temperature method. By using Cluster Perturbation Theory (CPT), the finite temperature spectral function is extended to the infinite system, clearly exhibiting the effects of spin-charge separation. [14,15]. In principle this method can be applied at all temperatures, but at low temperatures the required number of random samples is very large. FTLM is restricted to small systems and particularly at low temperatures, finite size effects become important. They can be overcome, at least for properties derived from the single particle Green's function, by using Cluster Perturbation Theory (CPT) [16,17], which provides infinite system results with remarkable accuracy [18]. However, CPT requires finite cluster Greens functions G ab (ω) for all sites a, b, increasing the number of required Lanczos runs and matrix elements by a factor equal to the number of lattice sites. It therefore requires a sufficiently fast low temperature method.In this paper we present a modified finite temperature Lanczos method which allows to calculate properties for large Hilbert spaces at low temperatures that are not accessible by the existing method. We show that a combination of our low temperature Lanczos method (LTLM) with the FTLM allows an accurate calculation of thermodynamic properties at any temperature with moderate effort.Let us first present the existing FTLM. For the case of a static expectation value of an operator Owith β = 1/T (k B =h = 1) and a sum over a complete orthonormal basis set |n , the FTLM approximation iswith a sum over symmetry sectors s of dimension N s , and R random vectors |r in each sector [19]. M is the number of Lanczos steps. For each random vector |r , a Lanczos procedure is performed, yielding M eigenenergies ε For dynamical correlation functions C(t) = A(t)B , FTLM calculatesHere, an initial vectoris used to generate additional eigenenergiesε and similarly for (3). Thus the ground state result will suffer from severe statistical fluctuations, although the exact (Lanczos) eigenvector |Ψ 0 is reached with every |r and one random vector should be sufficient. Yet, FTLM gets worse with decreasing temperature T .

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Theoretical study of the optical conductivity ofα′−NaV2O5

Cited by 28 publications

References 27 publications

Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

Charge ordering and optical transitions ofLiV2O5and
Konstantinović
¹
,
Dong
²
,
Ziaei
³

et al. 2001
Phys. Rev. B
12
1
13
0
View full text Add to dashboard Cite

Low-temperature Lanczos method for strongly correlated systems

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Theoretical study of the optical conductivity ofα′−NaV2O5

Cited by 28 publications

References 27 publications

Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

Nature of insulating state inNaV2O5above charge-ordering transition: A cluster dynamical mean-field study

Charge ordering and optical transitions ofLiV2O5andKonstantinović1, Dong2, Ziaei3 et al. 2001Phys. Rev. B121130View full textAdd to dashboardCite

Low-temperature Lanczos method for strongly correlated systems

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About

Charge ordering and optical transitions ofLiV2O5and
Konstantinović
¹
,
Dong
²
,
Ziaei
³

et al. 2001
Phys. Rev. B
12
1
13
0
View full text Add to dashboard Cite