We consider a model of strongly correlated eg electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO3. It is found that the classical orbital order with alternating occupied eg orbitals has a full rotational symmetry at orbital degeneracy, and the excitation spectrum derived using the linear spin-wave theory is gapless. The quantum (fluctuation) corrections to the order parameter and to the ground state energy restore the cubic symmetry of the model. By applying a uniaxial pressure orbital degeneracy is lifted in a tetragonal field and one finds an orbital-flop phase with a gap in the excitation spectrum. In two dimensions the classical order is more robust near the orbital degeneracy point and quantum effects are suppressed. The orbital excitation spectra obtained using finite temperature diagonalization of two-dimensional clusters consist of a quasiparticle accompanied by satellite structures. The orbital waves found within the linear spin-wave theory provide an excellent description of the dominant pole of these spectra.

The present understanding of the electronic and magnetic properties of α ′ -NaV2O5 is based on the hypothesis of strong charge disproportionation into V 4+ and V 5+ , which is assumed to lead to a spin-1/2 Heisenberg chain system. A recent structure analysis shows, however, that the V-ions are in a mixed valence state and indistiguishable. We propose an explanation for the insulating state, which is not based on charge modulation, and show that strong correlations together with the Heitler-London character of the relevant intermediate states naturally lead to antiferromagnetic Heisenberg chains. The interchain coupling is weak and frustrated, and its effect on the uniform susceptibility is small. Dedicated to J. Zittartz on the occasion of his 60th birthday PACS. 75.50.Ee -75.30.Et -75.40.Cx -75.40.Mg One-dimensional spin-1/2 Heisenberg antiferromagnets are expected to undergo a structural phase transition into a dimerized phase at low temperature accompanied by the opening of a spin gap[1]. This spin-Peierls transition was first observed in organic systems [2], but has found considerable experimental attention after its recent discovery in CuGeO 3 (T sp = 14K)[3]. The α ′ -phase of NaV 2 O 5 appears to be the second inorganic compound where a similar transition was observed with an even higher transition temperature T sp = 34K [4]. The size of the spin gap was determined by neutron scattering [5], Raman[6] and other experiments. The transition into the low-temperature dimerized structure was confirmed by X-ray scattering[5], NMR[7], thermal-expansion[8] yet the detailed deformation pattern is still unknown.Based on an early structure determination for α ′ -NaV 2 O 5[9], the current picture for the origin of the one-dimensional magnetic properties rests on the assumption of charge discommensuration into V 4+ and V 5+ chains[4,5,7,10,11]. In Fig.1 the V1 and V2 chains in b-direction would corre-

Recent optical conductivity σ(ω) experiments have revealed an anomalous spectral distribution in the ferromagnetic phase of the perovskite system La1−xSrxM nO3. Using finite temperature diagonalization techniques we investigate σ(ω) for a model that contains only the eg-orbital degrees of freedom. Due to strong correlations the orbital model appears as a generalized t-J model with anisotopic interactions and 3-site hopping. In the orbital t-J model σ(ω) is characterized by a broad incoherent spectrum with increasing intensity as temperature is lowered, and a Drude peak with small weight, consistent with experiment. Our calculations for two-dimensional systems, which may have some particular relevance for the double-layer manganites, show that the scattering from orbital fluctuations can explain the order of magnitude of the incoherent part of σ(ω) in the low temperature ferromagnetic phase. Moreover orbital correlation functions are studied and it is shown that x 2 -y 2 orbital order is prefered in the doped planar model at low temperature. PACS numbers: 75.10.-b 75.40.Cx 75.40.Gb 25.40.Fq

Using finite temperature diagonalization techniques it is shown that the quarter-filled t-J-V model on a trellis lattice structure provides a quantitative explanation of the highly anisotropic optical conductivity of the α ′ -NaV2O5 compound. The combined effects of the short-range Coulomb interaction and valence fluctuations of V-ions determine the main absorption and the fundamental gap. Inter-ladder hopping is necessary for the explanation of the anomalous in-gap absorption and generation of spectral weight at high energy. The role of valence fluctuations is explained in terms of the domain wall excitations of an anisotropic 2D Ising model in a transverse field close to criticality.

We investigate a planar model for the ferromagnetic (FM) phase of manganites, which develops orbital order of eg electrons with x 2 -y 2 -symmetry at low temperature. The dynamic structure factor of orbital excitations and the optical conductivity σ(ω) are studied with help of a finite-temperature diagonalization method. Our calculations provide a theoretical prediction for σ(ω) for the 2D FM state and are of possible relevance for the recently found A-type phase of manganites at high doping which consists of FM layers coupled antiferromagnetically. In the x 2 -y 2 ordered regime σ(ω) shows both a Drude peak and a gapped incoherent absorption due to a gap in the orbital excitations. , and as a consequence the conduction should be quasi-2D and the magnetic coupling between the layers small. This broken symmetry state has to be distinguished from the orbital structure of the 3D FM state realized at lower doping, where orbital correlations are expected to be liquid like [4,5]. The latter FM state shows a highly anomalous form of the optical conductivity [6][7][8] with a large incoherent absorption extending up to ω ∼ 1eV. It has been argued that the anomalous incoherent absorption is related to the orbital degree of freedom [4,5,9] and characteristic for an orbital liquid [4,5]. However there are also alternative scenarios which attribute the incoherent feature to Jahn-Teller polarons [7,8]. Comparable optical studies in the high doping regime where the orbital ordered A-phase is the stable ground state have not yet been reported. The purpose of this work is to present a theoretical analysis of the possible outcome of such experiments. The frequency dependence of σ(ω) is interesting since it is expected to reveal the orbital excitations in the doped x 2 -y 2 ordered phase, and may allow to distinguish between the orbital excitation and the Jahn-Teller polaron scenario.The evolution of x 2 -y 2 orbital order upon doping was also found in the study of planar models derived from the degenerate Kondo lattice model in the fully polarized FM phase [10]. Therefore we believe that this model is an appropriate starting point to investigate these questions. The t 2g -spins of the Mn 3+ and Mn 4+ ions as well the e g -electron spins of Mn 3+ are aligned globally in the FM-phase and can be integrated out. What remains is the orbital degree of freedom since there are two nearly degenerate e g orbitals per site. The large intra-atomic repulsive interactions prevent double occupancy of e g orbitals at the same site, which leads to a strong correlation problem and to nontrivial charge and orbital dynamics.For the saturated FM state the restriction to configurations without double occupancy leads to the orbital t-J model [11,10] (1)Here we use a and b (α and β) as orbital-pseudospin indices; whileā denotes the orthogonal e g orbital with respect to orbital a. A convenient basis is | ↑ = d x 2 −y 2 and | ↓ = d 3z 2 −r 2 . The transfer matrix elements are then given bywhich allows for inter-orbital hopping in the xy-plane. The ∓-sign...