Commensurate-incommensurate transition in two-coupled chains of nearly half-filled electrons

We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t _⊥ and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfinement crossover in this phase. A minimum of the charge gap is observed for values of t _⊥ close to this crossover. At large t _⊥ the region of the commensurate phase is enhanced, compared to a single chain. At the metal-insulator transition the Luttinger parameter takes the universal value K _ρ ^* = 1, in agreement with previous results on special limits of this model. Received 31 July 2000     

Quasiparticle bands in plane-chain coupled cuprates

The dispersion spectrum of single hole in a bilayer composed of plane and chain, each described by t-J model, coupled by - interactions between them, is calculated in terms of self-consistent Born approximation. It was found that for a weak interlayer coupling the two different quasiparticle bands, plane-like and chain-like bands, show a minimum at (, ) and a maximum at (0, 0) or (, ). In plane-like dispersion we can find an anomalous “flat” region near Fermi surface along the antiferromagnetic Brillouin zone boundary, which favors the formation of the van-Hove singularities. With increasing interlayer coupling, a large modification of the dispersions is carried out, the minimum deviates from (, ) and the energy gap of the two bands decreases and finally disappears when the vertical coupling is larger enough. The shapes of the QP bands are sensitive to the vertical hopping rather than the vertical exchange energy . As the interlayer coupling increases, the shapes of the two QP bands suggest that the chain-like band approaches to that of quasi-one dimensional model, and the plane-like band undergoes the one layer t - t '-J models' band. Received 17 March 1999     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution. Received: 9 May 1997 / Revised: 4 August 1997 / Accepted: 6 November 1997     

A model for the reflectivity spectra of TmTe

A simple one dimensional diatomic chain model is proposed to explain the reflectivity spectra of TmTe as observed by Wardet al. It is suggested that the system undergoes a structural phase transition of order-disorder type at 4.2 K, where the new phase assumes an anti-ferroelectric type of arrangement of the atoms. The results, we obtained, agree well qualitatively with the experimental results.     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Phase diagram of quasi-one-dimensional metals and superconductivity in the (TMTSF)2X compounds

The phase diagram of a quasi-one-dimensional metal is derived for a system with interchain tunneling. Retarded and nonretarded forward and backward scattering interactions are included. We show that singly charged acceptor molecules produce a potential along the conducting chains which leads to a retarded umklapp scattering. This umklapp scattering depends strongly on the phonon frequency and can explain the crossover of spin density wave to superconductivity as function of pressure as observed in (TMTSF)₂X compounds.     

Wave shape of de Haas-van Alphen oscillations and effective mass in the two-dimensional organic conductor α-(BEDT-TTF)2KHg(SCN)4

De Haas-van Alphen (dHvA) oscillations in the two dimensional organic conductor α-(BEDT-TTF)₂KHg(SCN)₄ have been measured by a canti-lever technique at high magnetic fields up to 30 T. The wave shape of the dHvA oscillations undergoes a drastic change around the transition field B_K (24 T). The effective mass shifts 1.5 m₀ in the density wave phase (B<B_K) to 1.65 m₀ in the normal metallic phase (B>B_K). Based on the simulation, we have determined that the primary cause of the characteristic field dependence of the wave shape is the change in the effective mass.     

Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion

Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L ² towards a 1/L decay when the Coulomb energy to Fermi energy ratio increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at . Received 13 March 2000     

The partition function of an interacting many body system

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. Received 28 March 2002 Published online 17 September 2002     

Specific heat behavior of high temperature superconductors in the pseudogap regime

We consider the competition between the one dimensionalization effect due to a magnetic field and the hopping parameters in quasi-one-dimensional conductors. Our study is based on a perturbative renormalization group method with three cut-off parameters, the bandwidth E₀, the 1D-2D crossover temperature T^*₁, which is related to the hopping process t₁, and the magnetic energy . We have found that the renormalized crossover temperatures T^*₁ and T^*₂, at which the respectively hopping processes t₁ and t₂ become coherent, are reduced compared to the bare values as the field is increased. We discuss the consequences of these renormalization effects on the temperature-field phase diagram of the organic conductors.Received: 5 March 2003, Published online: 23 July 2003PACS: 64.60.-i General studies of phase transitions - 75.30.Fv Spin-density waves - 72.15.Gd Galvanomagnetic and other magnetotransport effects - 74.70.Kn Organic superconductors     

Non-uniformities in polymer/liquid crystal mixtures

We theoretically model the nucleation of nematic droplets during phase ordering in mixtures of a flexible polymer and a low-molecular-weight liquid crystal. By appealing to classical nucleation theory (CNT), we calculate the energy barrier to nucleation and the size of a critical nucleus. We study the influence of a metastable intermediate phase on the nucleation of the nematic. Below a triple point in the phase diagram, there are two distinct mechanisms for the formation of a nematic nucleus: 1) direct nucleation from the isotropic phase and 2) nucleation via a precursor metastable isotropic phase. We calculate the crossover concentration as a function of temperature, delineating the regions of the phase diagram in which each mechanism prevails. In the latter case, the presence of a hidden metastable isotropic-isotropic binodal may either promote or delay the nucleation of a nematic phase. Received 9 August 2002 RID="a" ID="a"e-mail: matuyama@chem.mie-u.ac.jp     

Bethe ansatz study of 1+1 dimensional Hubbard model

A wave function of Bethe ansatz form is used to obtain approximate solutions for a 1+1 dimensional Hubbard model. In this model a helical structure with infinite diameter is constructed to mimic the square lattice. Betheansatz analysis is performed along the helical line. By including the hopping integrals in perpendicular direction, the solutions show some recovery of two dimensional character. At half-filling, the system undergoes Mott transition, the critical value of on-site repulsion obtained by this scheme is smaller than that of the mean-field theory. For a given particle density, the energy level of corresponding one dimensional model is extended to a band. The relation of the results to the properties of two dimensional strong-correlation system is discussed.     

Dynamics of a stochastically driven Brownian particle in one dimension

We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses slowly toward the second particle, labeled M. The displacements of particle M exhibits a crossover from diffusion to drift at a characteristic time which depends on the rate constants. We show that the positional fluctuation of M exhibits an intermediate crossover regime of subdiffusion separating initial and asymptotic diffusive behavior; this is in agreement with the complete set of Master Equations that describe the stochastic evolution of the model. The intermediate crossover regime can be considerably large depending on the hopping probabilities of the two particles. This is in contrast to the known crossover from diffusive to subdiffusive behavior of a tagged particle that is in the interior of a large single-file system on an unbound real line. We discuss our model with respect to the biological phenomena of membrane protrusions, where polymerizing actin filaments (F) push the cell membrane (M).     

Stability and diffusion of surface clusters

Using kinetic Monte Carlo simulations and a bond-counting ansatz, thermal stability and diffusion of an adatom island on a crystal surface are studied. At low temperatures, the diffusion constant D is found to decrease for a wide range of island sizes like , where is close to one, N being the number of adatoms in the cluster. By heating up the surface, the system undergoes a phase transition above which the island disappears. Characteristics of that transition are discussed. Received 20 January 1999     

Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction

The interplay between the quantum interferences responsible for one particle localization over a length L₁, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L ₂ > L ₁ , is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t₁ necessary to propagate over L₁, the interaction slows down the ballistic motion. On the contrary, after t₁ the interaction favors a very slow delocalization, characterized by a spreading of the center of mass, until L₂ is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U. Received 24 August 1998