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arXiv:1611.07861 · Physical review. B./Physical review. B

Charge ordering and correlation effects in the extended Hubbard model

Hanna Terletska, Tianran Chen, Emanuel Gull

Published Mar 27, 2017• 71 citations
arXivHTMLPDF

Abstract

We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.

DOI
10.1103/physrevb.95.115149

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We study the extended Hubbard model away from half filling on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size 8. We show that the model exhibits metallic, compressible charge-ordered, and insulating charge-ordered phases. We determine the location of the charge-ordering phase transition line at finite temperature and the properties of the phases as a function of doping, temperature, local interaction, and nearest-neighbor interaction. An analysis of the energetics of the charge-order transition shows that the charge-ordering transition mainly results in a rearrangement of local and nonlocal potential energy. We show the doping evolution of the spectral function from the isotropic metal via a charge-ordered metal to a charge-ordered insulator with a big gap, and study finite-size effects of the approximation.
We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\ifmmode\times\else\texttimes\fi{}2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction VVV causes ``screening'' effects close to the Mott phase transition, pushing the phase boundary to larger values of UUU. We also demonstrate the different effects of VVV on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.
We perform a thorough study of the extended Hubbard model featuring local and nearest-neighbor Coulomb repulsion. Using the dynamical mean-field theory we investigated the zero-temperature phase diagram of this model as a function of the chemical doping. The interplay between local and nonlocal interactions drives a variety of phase transitions connecting two distinct charge-ordered insulators, i.e., half filled and quarter filled, a charge-ordered metal and a Mott-insulating phase. We characterize these transitions and the relative stability of the solutions and we show that the two interactions conspire to stabilize the quarter-filled charge-ordered phase.
We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating antiferromagnetic state, as well as between the antiferromagnetic and charge-order states. We find hysteresis along the antiferromagnet/charge order and normal/charge-order phase boundaries (at larger values of the on-site interaction), indicating first-order phase transitions. We show that nearest-neighbor interactions lower the critical temperature for the antiferromagnetic phase. We also present results for the effect of nearest-neighbor interactions on the antiferromagnetic phase boundary and for the evolution of spectral functions and energetics across the phase transitions.
In this paper, we investigate the impact of nonlocal correlations on charge fluctuations in the two-dimensional single-band Hubbard model close to the Mott metal-to-insulator transition, employing the ladder dynamical vertex approximation. At half filling and for interaction strengths and temperatures where the system is in the Mott insulating phase, charge fluctuations are strongly suppressed. Under these conditions, dynamical mean-field theory (DMFT) calculations predict a strong enhancement of the charge susceptibility at small (electron or hole) doping. However, these DMFT results include only the effects of purely local correlations despite the importance of nonlocal correlations in two-dimensional systems. We have, hence, carried out ladder dynamical vertex approximation $(\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A})$ simulations which allow for the inclusion of such nonlocal correlation effects while retaining the local ones of DMFT. Our $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ numerical data show that close to half filling the large uniform charge susceptibility of DMFT is strongly suppressed by nonlocal fluctuations but gradually increases with (electron) doping. At a certain doping value, charge fluctuations eventually become larger in $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ with respect to DMFT, indicating that the absence of nonlocal correlations underestimates the mobility of the charge carriers in this parameter regime. This metallization effect is also reflected in an enhancement of the $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ kinetic and potential energies and a corresponding reduction of the (absolute value of the) $\mathrm{lD}\mathrm{\ensuremath{\Gamma}}\mathrm{A}$ Matsubara self-energy with respect to DMFT.
We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half-filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalization of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions $U\ensuremath{\geqslant}3t$. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.