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Kluwer Academic Publishers eBooks

Dynamical Mean-Field Theory of Stripe Ordering

Alexander I. Lichtenstein, Marcus Fleck, Andrzej M. Oleś, Lars Hedin

Published Mar 29, 2006• 0 citations
Publisher

Abstract

Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47100-0_12

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Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped $(\ensuremath{\delta}=1/8)$ and overdoped $(\ensuremath{\delta}=1/4)$ systems. At intermediate values of U in underdoped systems $(\ensuremath{\delta}=1/8)$ local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped $(\ensuremath{\delta}=1/4)$ systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.
We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where ddd-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
The internal structure of stripes in the two-dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes with inhomogeneous magnetization and charge along the stripe core, consistent with experimental observations, are stabilized by quantum fluctuations, included through the configuration interaction method. Similar configurations result to be stable for filled stripes, and have a lower energy than the standard paramagnetic core solution. Away from half-filling, solitonlike solutions show up within the Hartree-Fock approximation. The hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The hole-hole correlation shows maxima along the stripe direction, while the integrated value of ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ compares satisfactorily with experimental results.
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (UUU---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
The optical conductivity of the weakly doped two-dimensional repulsive Hubbard model on the square lattice with the nearest and next-nearest hoppings is calculated within the generalized dynamical mean-field $(\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}})$ approach, which includes correlation length scale $\ensuremath{\xi}$ into the standard DMFT equations via the momentum dependent self-energy ${\ensuremath{\sum}}_{\mathbf{p}}$, with a full account of appropriate vertex corrections. This approach takes into consideration the nonlocal dynamical correlations induced, e.g., by short-ranged collective spin-density-wavelike antiferromagnetic spin fluctuations, which (at high enough temperatures) can be viewed as a quenched Gaussian random field with finite correlation length $\ensuremath{\xi}$. The DMFT effective single-impurity problem is solved by numerical renormalization group. We consider both the case of correlated metal with the bandwidth $W\ensuremath{\lesssim}U$ and that of doped Mott insulator with U⪢WU⪢WU⪢W (UUU---the value of local Hubbard interaction). The optical conductivity calculated within $\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}}$ demonstrates typical pseudogap behavior within the quasiparticle band, in qualitative agreement with experiments in copper oxide superconductors. For large values of UUU, pseudogap anomalies are effectively suppressed.