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arXiv:cond-mat/0203580 · Physical review. B, Condensed matter

dx2−y2 density-wave order and its role in the phase diagram of extended Hubbard models

Chetan Nayak, Eugene Pivovarov

Published Aug 13, 2002• 30 citations
arXivHTMLPDF

Abstract

We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest-neighbor interaction and correlated hopping. The underdoped region of the phase diagram features ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic order. For larger doping, it coexists with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity. While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.

DOI
10.1103/physrevb.66.064508

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We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest-neighbor interaction and correlated hopping. The underdoped region of the phase diagram features dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic order. For larger doping, it coexists with dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ superconductivity. While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.
We consider an extended Hubbard model with nearest-neighbor correlated hopping and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ obtained as an effective model for cuprate superconductors. Using a generalized Hartree-Fock BCS approximation, we find that for high enough ${t}^{\ensuremath{'}}$ and doping, antiferromagnetism is destroyed and the system exhibits d-wave superconductivity. Near optimal doping we consider the effect of antiferromagnetic spin fluctuations on the normal self-energy using a phenomenological susceptibility. The resulting superconducting critical temperature as a function of doping is in good agreement with experiment.
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.
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dx2−y2d_{x^{2} - y^{2}}dx2−y2​-Density Wave and dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave Superconducting Gap on the Extended Hubbard Model on a Square Lattice: Approach to Finite Temperature Properties
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We study the square-lattice extended Hubbard model with on-site UUU and nearest-neighbor VVV interactions by exact diagonalization. We show that nonequilibrium quench dynamics can help determine the equilibrium phase transition boundaries, which agree with the calculations of the fidelity metric, dynamical structure factor, and correlation function. At half filling, the phase diagrams in the strong-coupling regime include spin density wave and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity at large positive UUU, charge density wave (extended s∗{s}^{*}s∗-wave superconductivity) at large positive (negative) VVV, and sss-wave superconductivity at large negative UUU with vanishing VVV. The energies of different particle sectors also help determine the phase separation region. With carrier doping, charge fluctuation results in a strong competition between different orders, making it more difficult to identify the leading instability on finite-size clusters. Nevertheless, the more exotic ppp-wave superconducting pairing is found to be enhanced when the system is heavily overdoped by 37.537.5%--50%37.5 holes, especially in the interaction parameter range relevant to the cuprate superconductors.