Dynamics of a hole in the large--U Hubbard model: a Feynman diagram approach

We study the dynamics of a single hole in an otherwise half--filled two--dimensional Hubbard model by introducing a nonlocal Bogolyubov transformation in the antiferromagnetic state. This allows us to rewrite the Hamiltonian in a form that makes a separation between high--energy processes (involving double--occupancy) and low--energy physics possible. A diagrammatic scheme is developped that allows for a systematic study of the different processes delocalizing a carrier in the antiferromagnetic state. In particular, the so--called Trugman process, important if transverse spin fluctuations are neglected, is studied and is shown to be dominated by the leading vertex corrections. We analyze the dynamics of a single hole both in the Ising limit and with spin fluctuations. The results are compared with previous theories as well as with recent exact small--cluster calculations, and we find good agreement. The formalism establishes a link between weak and strong coupling methodologies.Comment: Latex 34pages, Orsay Preprint, submitted to Phys. Rev.

Theory of the Reentrant Charge-Order Transition in the Manganites

A theoretical model for the reentrant charge-order transition in the manganites is examined. This transition is studied with a purely electronic model for the Mn electrons: the extended Hubbard model. The electron-phonon coupling results in a large nearest-neighbor repulsion between electrons. Using a finite-temperature Lanczos technique, the model is diagonalized on a 16-site periodic cluster to calculate the temperature-dependent phase boundary between the charge-ordered and homogeneous phases. A reentrant transition is found. The results are discussed with respect to the specific topology of the 16-site cluster.Comment: 3 pages, 2 ps figures included in text, submitted to the 8th MMM-Intermag conferenc

Quantum fluctuations in the spiral phase of the Hubbard model

We study the magnetic excitations in the spiral phase of the two--dimensional Hubbard model using a functional integral method. Spin waves are strongly renormalized and a line of near--zeros is observed in the spectrum around the spiral pitch $\pm{\bf Q}$. The possibility of disordered spiral states is examined by studying the one--loop corrections to the spiral order parameter. We also show that the spiral phase presents an intrinsic instability towards an inhomogeneous state (phase separation, CDW, ...) at weak doping. Though phase separation is suppressed by weak long--range Coulomb interactions, the CDW instability only disappears for sufficiently strong Coulomb interaction.Comment: Figures are NOW appended via uuencoded postscript fil

On the universal Representation of the Scattering Matrix of Affine Toda Field Theory

By exploiting the properties of q-deformed Coxeter elements, the scattering matrices of affine Toda field theories with real coupling constant related to any dual pair of simple Lie algebras may be expressed in a completely generic way. We discuss the governing equations for the existence of bound states, i.e. the fusing rules, in terms of q-deformed Coxeter elements, twisted q-deformed Coxeter elements and undeformed Coxeter elements. We establish the precise relation between these different formulations and study their solutions. The generalized S-matrix bootstrap equations are shown to be equivalent to the fusing rules. The relation between different versions of fusing rules and quantum conserved quantities, which result as nullvectors of a doubly q-deformed Cartan like matrix, is presented. The properties of this matrix together with the so-called combined bootstrap equations are utilised in order to derive generic integral representations for the scattering matrix in terms of quantities of either of the two dual algebras. We present extensive case-by-case data, in particular on the orbits generated by the various Coxeter elements.Comment: 57 page

On the metal-insulator transition in the two-chain model of correlated fermions

The doping-induced metal-insulator transition in two-chain systems of correlated fermions is studied using a solvable limit of the t-J model and the fact that various strong- and weak-coupling limits of the two-chain model are in the same phase, i.e. have the same low-energy properties. It is shown that the Luttinger-liquid parameter K_\rho takes the universal value unity as the insulating state (half-filling) is approached, implying dominant d-type superconducting fluctuations, independently of the interaction strength. The crossover to insulating behavior of correlations as the transition is approached is discussed.Comment: 7 pages, 1 figur

Competitive density waves in quasi-one-dimensional electron systems

We investigate the nature of the ground state of the one-dimensional t-J model coupled to adiabatic phonons by use of the Lanczos technique at quarter filling. Due to the interplay between electron-electron and electron-phonon interactions, the model undergoes instabilities toward the formation of lattice and charge modulations. Moderate on-site and intra-site electron-phonon couplings lead to a competition of different spin-Peierls and dimerized states. In the former case two electrons belong to the unit cell and we expect a paramagnetic band insulator state, while lattice dimerization leads to a Mott insulating state with quasi long range antiferromagnetic order. The zero temperature phase diagram is obtained as a function of intra-site and inter-site electron-phonon couplings, analytically in the $J\to 0$ limit and numerically at finite J/t.Comment: 7 pages, 7 figures, to be published in Phys. Rev.

Resonant tunneling through protected quantum dots at phosphorene edges

We theoretically investigate phosphorene zigzag nanorribons as a platform for constriction engineering. In the presence of a constriction at the upper edge, quantum confinement of edge protected states reveals resonant tunnelling Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower edge. Coupling between edges in thin constrictions gives rise to Fano-like and anti-resonances in the transmission spectrum of the system.Comment: 8 pages,7 figure

Localized electron state in a T-shaped confinement potential

We consider a simple model of an electron moving in a T-shaped confinement potential. This model allows for an analytical solution that explicitly demonstrates the existence of laterally bound electron states in quantum wires obtained by the cleaved edge overgrowth technique.Comment: 6 pages, 5 figure