Competing Phases and Basic Mechanisms in Strongly-interacting Electron Systems

Download or read book Competing Phases and Basic Mechanisms in Strongly-interacting Electron Systems written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this work was to continue the effort to develop numerical tools in order to understand the properties of strongly-correlated electron materials. Towards this goal, they developed new stochastic series Monte Carlo techniques to study the phases of a two-dimensional quantum XY model with ring exchange in an external magnetic field. They determined the zero-temperature phase diagram of this model and found two quantum phase transitions. The first was between an XY-ordered phase and a striped valence-bond phase. The second was between the valence-bond phase and a staggered Neel antiferromagnetic phase. With the external field as an additional control parameter they were able to conclude that this system did not show a quantum spin liquid phase. They extended the study of the Xy model with ring exchange to study its behavior in the 3 dimensions. They find that in three dimensions, the superfluid phase persists to asymptotically large values of the ring exchange K. they do find exotic fractionalized phases in three dimensions. The role of the electron-phonon coupling in the cuprates remains open. They have studied the effect of an onsite Hubbard U Coulomb interaction on the electron-phonon vertex. They found that at strong coupling, Coulomb interaction caused the electron-phonon interaction to be suppressed at large momentum transfers leading to an effective peaking of the interaction in the forward direction while for weaker values of U, the electron-phonon interaction was simply suppressed at all q values. This behavior could favor d-wave pairing, although the effective pairing strength of the phonons remains weak in this model. The dynamics of the pairing interaction is reflected in the frequency dependence of the gap. They have used exact diagonalization to study the frequency dependence of the gap for a two-leg t-J ladder. They were able to determine both the real and imaginary parts of the gap. The key observation was that the weight of the imaginary part was sufficient to account for most all of Re[Delta] (k, [omega] = 0), implying that the dynamics of the interaction is not set by the Mott-Hubbard gap (which is infinite for the t-J model).