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Journal of Physics Condensed Matter

Competition between charge and bond waves in a Peierls-Hubbard model

Jaime Rössler, D Gottlieb

Published Apr 23, 1990• 3 citations
Publisher

Abstract

The authors study a one-dimensional extended Hubbard-Peierls model in the infinite intracell Coulomb repulsion limit, which is equivalent to a system of spinless electrons. They consider first- and second-neighbor Coulomb repulsion, and two types of phonon are coupled to the electronic system: intramolecular and longitudinal, intercell vibrations. The special case of half an electron per cell is considered. The model is solved in the Hartree-Fock approximation by assuming a possible symmetry break of period two. The solution is obtained for all temperatures. They construct a phase diagram with respect to temperature and the system parameters. Three types of low temperature ordered phase appear: bond ordered waves (BOW), charge ordered waves (COW) and an intermediate phase, across which the transition BOW to COW is continuous. This phase corresponds to a ferroelectric state (F). As temperature is increased from zero, the system undergoes different phase transitions, following a particular sequence, according to its characteristic parameters. At high temperatures the system stabilises in a homogeneous (disordered) phase (H). For some parameters the sequence BOW to F to COW to H is possible. The last result is very striking, since it implies that, on increasing temperature, the symmetry of the system can decrease, as is the case for the BOW to F transition, where the inversion symmetry is lost. This special BOW to F phase transition also occurs in the non-interacting limit, where the results are exact.

DOI
10.1088/0953-8984/2/16/003

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The authors study a one-dimensional extended Hubbard-Peierls model in the infinite intracell Coulomb repulsion limit, which is equivalent to a system of spinless electrons. They consider first- and second-neighbor Coulomb repulsion, and two types of phonon are coupled to the electronic system: intramolecular and longitudinal, intercell vibrations. The special case of half an electron per cell is considered. The model is solved in the Hartree-Fock approximation by assuming a possible symmetry break of period two. The solution is obtained for all temperatures. They construct a phase diagram with respect to temperature and the system parameters. Three types of low temperature ordered phase appear: bond ordered waves (BOW), charge ordered waves (COW) and an intermediate phase, across which the transition BOW to COW is continuous. This phase corresponds to a ferroelectric state (F). As temperature is increased from zero, the system undergoes different phase transitions, following a particular sequence, according to its characteristic parameters. At high temperatures the system stabilises in a homogeneous (disordered) phase (H). For some parameters the sequence BOW to F to COW to H is possible. The last result is very striking, since it implies that, on increasing temperature, the symmetry of the system can decrease, as is the case for the BOW to F transition, where the inversion symmetry is lost. This special BOW to F phase transition also occurs in the non-interacting limit, where the results are exact.
The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion UUU promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-UUU Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger UUU, the two transitions merge at a tricritical point into a single first-order Mott/Peierls transition. In addition, we show that an intermediate phase also occurs in the quarter-filled model.
In this paper, by using the level spectroscopy method and bosonization theory, we discuss the evolution of the bond-order-wave (BOW) phase in a one-dimensional half-filled extended Hubbard model with the on-site Coulomb repulsion U as well as the inter-site Coulomb repulsion V and antiferromagnetic exchange J . After clarifying the generic phase diagrams in three limiting cases with one of the parameters being fixed at zero individually, we find that the BOW phase in the U-V phase diagram is initially enlarged as J increases from zero but is eventually suppressed as J increases further in the strong-coupling regime. A three-dimensional phase diagram is suggested where the BOW phase exists in an extended region separated from the spin-density-wave and charge-density-wave phases.
We study the nature of the ground state of a one-dimensional electron-phonon model for molecular crystals: The phonons are assumed dispersionless and couple to the local electronic density. We consider the half-filled-band sector and discuss the stability of the Peierls-dimerized ground state as a function of the phonon frequency ($\ensuremath{\omega}$), electron-phonon coupling constant ($\ensuremath{\lambda}$), and number of components of the electron spin (nnn). First, we discuss the properties of the model in the limiting cases of zero frequency and infinite frequency. We then perform a strong coupling expansion which maps the system onto a spinless fermion model with nearest-neighbor repulsion for both spinless and spin-\textonehalf{} electrons, but with different parameters in both cases. Finally, we perform a numerical study of the system using a Monte Carlo technique. We study the behavior of the order parameter and of correlation functions for various points in parameter space. We also perform a finite-size---scaling analysis of the numerical data. The conclusions of our study are the following: For the case of spinless electrons, there exists always a disordered phase for small coupling constant, and the system undergoes an infinite-order transition to a Peierls-dimerized state as the coupling constant increases beyond a critical value. The phase diagram is divided between a disordered and an ordered region by a line that connects the points ($\ensuremath{\omega}=0$, $\ensuremath{\lambda}=0$) and ($\ensuremath{\omega}=\ensuremath{\infty}$, $\ensuremath{\lambda}=\ensuremath{\infty}$). For the case of spin-\textonehalf{} electrons, the system is dimerized for arbitrary $\ensuremath{\lambda}$ and $\ensuremath{\omega}$ except in the limit $\ensuremath{\omega}=\ensuremath{\infty}$.
The Hubbard-Holstein model is one of the central models that describe the competition between electron-electron and electron-phonon interactions. In one dimension and at half-filling, the interplay between an electronic spin-density wave and a phonon-driven charge-density wave is considered to stabilize an intermediate Luther-Emery liquid. Here we show that, once the extended metallic regime disappears, a narrow bond-order-wave phase emerges. We use an exact directed-loop quantum Monte Carlo method for retarded interactions to simulate system sizes of several hundred sites, necessary to observe the weak signatures of this novel phase. Our results suggest a second-order quantum phase transition between the two charge orders that only turns first-order at strong coupling. Our findings are reminiscent of the extended Hubbard model, but they are driven by competing frequency dependencies of the same dynamically-screened Hubbard interaction.
The two-dimensional Peierls-Hubbard model is studied at half filling within both Hartree-Fock and Kotliar-Ruckenstein slave-boson theory. The interplay between two types of long-range order, bond-order wave (BOW) and antiferromagnetism (AFM), is analyzed for two representative dimerization patterns, corresponding both to the same wave vector $(\ensuremath{\pi},\ensuremath{\pi}).$ For each pattern, the Peierls dimerization (and associated BOW) is weakened and finally suppressed with increasing Hubbard on-site interaction, and correspondingly AFM is gradually enhanced. In particular, a coexistence regime with both BOW and AFM order is established in the parameter space of electron-lattice and Hubbard interactions.
We study the competition between an instantaneous local Coulomb repulsion and a boson mediated retarded attraction, as described by the Hubbard-Holstein model. Restricting to the case of half-filling, the ground-state phase diagram and the transitions from antiferromagnetically ordered states to charge ordered states are analyzed. The calculations are based on the model in large dimensions, so that dynamical mean-field theory can be applied, and the associated impurity problem is solved using the numerical renormalization group method. The transition is found to occur when electron-electron coupling strength UUU and the induced interaction $\ensuremath{\lambda}$ due to electron-phonon coupling approximately coincide, $U\ensuremath{\simeq}\ensuremath{\lambda}$. We find a continuous transition for small coupling and large ${\ensuremath{\omega}}_{0}$, and a discontinuous one for large coupling and/or small ${\ensuremath{\omega}}_{0}$. We present results for the order parameters, the static expectation values for the electrons and phonons, and the corresponding spectral functions. They illustrate the different types of behavior to be seen near the transitions. Additionally, the quasiparticle properties are calculated in the normal state, which leads to a consistent interpretation of the low-energy excitations.