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arXiv:cond-mat/0605091 · Physical Review B

Competitive density waves in quasi-one-dimensional electron systems

Samuele Bissola, Alberto Parola

Published May 9, 2006• 2 citations
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Abstract

We investigate the nature of the ground state of the one-dimensional $t\text{\ensuremath{-}}J$ 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 intrasite 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 intrasite and intersite electron-phonon couplings, analytically in the $J\ensuremath{\rightarrow}0$ limit and numerically at finite $J∕t$.

DOI
10.1103/physrevb.73.195108

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We investigate the nature of the ground state of the one-dimensional t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-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 intrasite 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 intrasite and intersite electron-phonon couplings, analytically in the J\ensuremath→0J\ensuremath{\rightarrow}0J\ensuremath→0 limit and numerically at finite J∕tJ∕tJ∕t.
The ground state of the one-dimensional $t\text{\ensuremath{-}}J$ model coupled with phonons in the adiabatic limit is numerically investigated by use of the Lanczos technique at quarter filling. Due to the interplay between the electron-electron Coulomb repulsion and electron-phonon interaction, this model shows a sequence of lattice distortions leading to the formation of charge-density waves and bond-order waves. Moderate electron-electron and electron-lattice coupling may lead to the coexistence of dimerization and tetramerization in the distortion pattern. Dimerization leads to the formation of an ``antiferromagnetic'' Mott insulator, while tetramerization gives rise to a spin-Peierls phase. By increasing the super exchange coupling, antiferromagnetism is inhibited due to the change of the distortion periodicity.
We present exact results for the ground-state properties of the two-dimensional single-hole Peierls t-J model on finite square lattices, up to 18 effective sites in size. Using a Lanczos technique for unrestricted energy minimization with respect to local lattice distortions, we study the competition between intrasite electron-phonon and intersite antiferromagnetic (AFM) exchange coupling on the hole state over a wide range of interaction strengths. The structure of the doping state is examined by calculating local expectation values of spin and electron densities as well as magnetic and charge correlation functions. As the local electron-phonon interaction increases, we find a self-trapping transition from a delocalized hole (polaronlike) state to a mainly localized hole state. Despite a weak lattice distortion the delocalized case has similar properties to the ground state of the pure t-J model, whereas the localized hole state exhibits strong local lattice distortion and a quenched magnetic moment coupled ferromagnetically to an otherwise unperturbed AFM background. Aspects of the phase diagram are discussed.
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling ggg to the phonons drives the system towards a Peierls charge density wave state, whereas increasing the electron-electron interaction UUU drives the fermions into a Mott antiferromagnet. At low ggg and UUU, or when doped, the system is metallic. In one dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long-range coupling to phonons, with characteristic range $\ensuremath{\xi}$, interpolating between the Holstein and Fr\"ohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $\ensuremath{\xi}$ and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction UUU will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U\ensuremath{\ne}0$ case, even for small values of the coupling range.
As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra, and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multiquanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin- and charge-excitation gaps by a finite-size scaling analysis based on density-matrix renormalization-group calculations.
We study the one-dimensional Holstein model with spin-12\frac{1}{2}21​ electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
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.