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We propose the origin of the charge-ordered stripe structure with the orbital ordering observed experimentally in La 12x Ca x MnO 3 (x 1͞2, 2͞3), in which the long-range Coulomb interaction plays an essential role. We study a Hubbard model with doubly degenerate e g orbitals, and treat the on-site Coulomb interaction (U) and the nearest-neighbor interaction (V ) with the Hartree-Fock approximation. Both the charge and orbital ordering structures observed in experiments are reproduced for a wide region of the U-V phase diagram. The stability of the orbital ordering is also confirmed by perturbation theory. PACS numbers: 71.20.Be, 71.10.Fd In some perovskite-type hole-doped manganese oxides R 12x A x MnO 3 (R: rare earth elements, A: alkaline earth elements), the colossal magnetoresistance effect has been the subject of intense studies. Recently, characteristic charge-ordering phenomena in these materials have also attracted a growing interest. Especially, in La 12x Ca x MnO 3 for x 1͞2 and 2͞3, it has been reported that the chargeorbital stripe (COS) structure occurs in some periodicities which correspond to commensurate concentrations [1][2][3][4][5][6].Concerning the pure LaMnO 3 system (x 0), the antiferromagnetic (AF) insulating phase appears [7], where the orbital ordering accompanied with the Jahn-Teller (JT) distortion coexists because of the JT active ion Mn 13 [8,9]. In the same way, it is suggested that the JT effect is also the origin of the stripe structure in the systems with finite carrier concentrations such as x 1͞2 and 2͞3 [5,10]. According to this scenario, however, a considerably strong JT effect is necessary to realize the insulating COS structure [10]. In this sense, it is insufficient to ascribe the origin of the stripe structure only to the JT effect.In the present Letter, we show that the COS structure observed in the La 12x Ca x MnO 3 can be explained only by considering the Coulomb interaction between carriers.We study a Hubbard model with doubly degenerated orbitals which correspond to e g orbitals on Mn ions. By treating the Coulomb interaction with the Hartree-Fock approximation, we investigate the stability of the COS structure observed in experiments for the x 1͞2 system [ Fig. 1(a)] [1,2,11] and the x 2͞3 system [ Fig. 1(b)] [6,11], and discuss another type of charge ordering found by an electron microscopy study reported in Ref. [5] [ Fig. 1(c)]. We show that the COS structure appears for a realistic strength of on-site and nearest-neighbor Coulomb interactions. In particular, we emphasize that the nearestneighbor Coulomb interaction is indispensable for the occurrence of the stripe structure with the orbital ordering.Several authors have previously studied the effect of the on-site Coulomb interaction on the orbital ordering in manganese oxides [12][13][14][15]. Especially, in the x 0 system, it was shown that the orbital ordering is stabilized by the on-site Coulomb interaction [14]. However, the effects of the long-range Coulomb interaction have not been studied enough.The ch...

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We have found an error in the calculation of imaginary-time one-particle Green's functions G͑t͒ by the finitetemperature density-matrix renormalization-group method. The problem is concerned with the counting of the fermionic sign and the two-particle correlation functions were calculated correctly. Although the main conclusions of the Letter do not change, the density of states shown in Fig. 1 should be replaced by the ones in the new Fig. 1. The gap edge of the spectrum at the lowest temperature is not modified.The spectra have intensities in the region jvj & 3, which is reduced considerably from the original results. However, the reason that the spectral weight extends beyond the original bandwidth remains the same: the exchange interaction between the conduction electrons and the f spins. The important conclusion about the temperature dependence of the spectrum also remains the same: With increasing temperature, the low-frequency structure varies drastically at a much lower temperature than D qp 0.7t, and the gap structure disappears at T Ӎ 0.3t.FIG. 1. Spectra of single-particle excitations r͑v͒ at various temperatures.