We study the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion (U and V , respectively) in the Dynamical Mean Field theory. At quarter filling, the model shows a transition to a charge ordered phase with different sublattice occupancies nA = nB. The effective mass increases drastically at the critical V and a pseudo-gap opens in the single-particle spectral function for higher values of V . The Vc(T )-curve has a negative slope for small temperatures, i.e. the charge ordering transition can be driven by increasing the temperature. This is due to the higher spin-entropy of the charge ordered phase.PACS 71.10.Fd, 71.27.+a, 71.45.Lr The possibility of crystallization of electrons due to their long-range Coulomb repulsion was first proposed by Wigner [1]. He considered an electron system in a uniform positive background at sufficiently low densities. The Wigner lattice is formed when the gain in Coulomb energy due to the localization of the electrons exceeds the gain in kinetic energy for the homogeneous electron distribution. It is experimentally realized in the two dimensional electron gas in a GaAs/AlGaAs heterostructure [2]. Due to the reduced dimensionality, the effect of the Coulomb interaction is enhanced so that the transition to the ordered state occurs at experimentally accessible electron densities.Crystallization of charge carriers (charge ordering) can also be observed in three dimensional systems, even at very high densities [3]. Here the kinetic energy of the electrons or holes has to be reduced drastically for the charge ordered state to become possible. In 4f-electron systems it is the small hybridization of the well localized 4f-orbitals that leads to a reduced kinetic energy. An example is Yb 4 As 3 where a first order charge ordering transition occurs at T c ≈ 295K [4,5]. The carrier concentration in Yb 4 As 3 (approximately one hole per four Yb ions) is considerably larger than typical values for a Wigner lattice. The kinetic energy of the electrons can also be reduced by the interaction with lattice and spin degrees of freedom. An interplay of these mechanisms is responsible for the charge order transition occurring in a variety of rare earth manganites (e.g., in La 1−x Ca x MnO 3 for x ≥ 0.5 [6]).In all examples mentioned so far, the charge ordered phase is the ground state. However, a melting of the charge ordered state on decreasing the temperature (i.e. a reentrant transition) has been found recently in In this Letter, we investigate the simplest model which allows for a charge ordering transition due to the competition between kinetic and Coulomb energy. The extended Hubbard model [9]describes fermions on a lattice with an on-site Coulomb repulsion U , a nearest neighbor Coulomb repulsion V and a hopping matrix element t. The c † iσ (c iσ ) denote creation (annihilation) operators for a fermion at site i with spin σ, the n i are defined as n i = n i↑ + n i↓ where n iσ = c † iσ c iσ and indicates the sum over nearest neighbors.In the following we study ...

We investigate a periodic Anderson model with interacting conduction electrons which are described by a Hubbard-type interaction of strength Uc. Within dynamical mean-field theory the total Hamiltonian is mapped onto an impurity model, which is solved by an extended non-crossing approximation. We consider the particle-hole symmetric case at half-filling. Similar to the case Uc = 0, the low-energy behavior of the conduction electrons at high temperatures is essentially unaffected by the f electrons and for small Uc a quasiparticle peak corresponding to the Hubbard model evolves first. These quasiparticles screen the f moments when the temperature is reduced further, and the system turns into an insulator with a tiny gap and flat bands. The formation of the quasiparticle peak is impeded by increasing either Uc or the c-f hybridization. Nevertheless almost dispersionless bands emerge at low temperature with an increased gap, even in the case of initially insulating host electrons. The size of the gap in the one-particle spectral density at low temperatures provides an estimate for the low-energy scale and increases as Uc increases. 71.27.+a,75.20.Hr,71.10.Fd

We use the dynamical mean-field method to determine the origin of the large ratio of the zero temperature gap to the transition temperature observed in most charge density wave materials. The method is useful because it allows an exact treatment of thermal fluctuations. We establish the relation of the dynamical mean-field results to conventional diagrammatics and thereby determine that in the physically relevant regime the origin of the large ratio is a strong inelastic scattering.Density wave ordering is a transition to a phase in which the electronic charge or spin density has lower symmetry than the underlying lattice. It occurs in a wide range of materials, including quasi-one-dimensional organic conductors [6]. Much recent activity has related to actual or possible 'stripe' density wave order in some members of the high temperature superconductor family [7] and to charge and orbital order in some members of the 'colossal' magnetoresistance materials [8].In most cases the density wave order evolves out of a metallic phase and in this situation it is usually believed [1] to be driven by a fermi surface 'nesting' instability. The resulting equations are similar to those of the 'BCS' theory of superconductivity and in particular lead to a ratio of T = 0 density wave gap ∆ to density wave ordering temperature T c which is close to the 'BCS' value ∆ BCS /k B T c = 1.76. Almost all density wave materials, however, exhibit much larger ∆/k B T c ratios. In quasione-dimensional materials the large ratio may be understood [1] as a consequence of critical fluctuations in low dimensionality, which decrease the transition temperature more than the T = 0 gap ∆. (Indeed, in a strictly one dimensional material, T c = 0 while ∆ > 0). However, ∆/T c values as large as 10 are also observed in quasi two dimensional systems and in many fully three dimensional materials [2,3,5,6]. These are not explicable either in the BCS approximation or in terms of the Migdal-EliashbergMcMillan generalization [9] to so-called strong coupling superconductors such as Pb, which exhibit ∆/T c ratios only as large as 2.5.A generally accepted explanation in the physically relevant regime has not appeared. An extremely large electron-phonon interaction could localize carriers as polarons with a large activation gap; the ordering temperature T c would then be controlled by a weak polaronpolaron repulsion and a large gap to T c ratio would result.However, this would imply a non-metallic normal state with a resistivity which is large and diverges rapidly as T → 0, unlike the systems listed above (except perhaps for Fe 3 O 4 ). McMillan made the intriguing suggestion (which has not been followed up by subsequent workers as far as we know) that the low T c (relative to ∆) was a phonon entropy effect [10]: thermal fluctuations of the phonons would create areas where the local gap was small compared to the average, and a self consistent process of exciting the electrons into these areas would lead to the destruction of long ranged order.In this paper we a...

We use the dynamical mean-field method to calculate the charge density wave transition temperature of the half-filled Holstein model as function of typical phonon frequency in the physically relevant adiabatic limit of phonon frequency Ω much less than electron bandwidth t. Our work is the first systematic expansion of the charge density wave problem in Ω/t. Quantum phonon effects are found to suppress Tco severely, in agreement with previous work on one dimensional models and numerical studies of the dynamical mean field model in the extreme antiadiabatic limit (Ω ∼ t). We suggest that this is why there are very few CDW systems with mean-field transition temperatures much less than a typical phonon frequency. 71.45.Lr,71.10.Fd,71.10.Hf

We propose a semiclassical approach based on the dynamical mean-field theory to treat the interactions of electrons with local lattice fluctuations. In this approach the classical ͑static͒ phonon modes are treated exactly, whereas the quantum ͑dynamical͒ modes are expanded to the second order and give rise to an effective semiclassical potential. We determine the limits of validity of the approximation, and demonstrate its usefulness by calculating the temperature dependent resistivity in the Fermi-liquid to polaron crossover regime ͑leading to ''saturation behavior''͒ and also isotope effects on electronic properties including the spectral function, resistivity, and optical conductivity, problems beyond the scope of conventional diagrammatic perturbation theories.