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arXiv:cond-mat/0403093 · Physical Review B

Phase diagram and quasiparticle properties of the Hubbard model within cluster two-site dynamical mean-field theory

E. C. Carter, A. J. Schofield

Published Jul 20, 2004• 16 citations
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Abstract

We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's ``two-site'' method [Phys. Rev. B. 64, 165114 (2001)], where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half-filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electronlike Fermi surface away from the Mott transition, to a holelike one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface, close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-${T}_{c}$ superconductors). This leaves Fermi arcs that are closed into pockets by lines with very small quasiparticle residue.

DOI
10.1103/physrevb.70.045107

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We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's ``two-site'' method [Phys. Rev. B. 64, 165114 (2001)], where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half-filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electronlike Fermi surface away from the Mott transition, to a holelike one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface, close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-Tc{T}_{c}Tc​ superconductors). This leaves Fermi arcs that are closed into pockets by lines with very small quasiparticle residue.
Cluster dynamical mean-field and maximum entropy analytical continuation methods are used to obtain theoretical estimates for the many-body density of states, electron self-energy, in-plane and ccc-axis optical conductivity and the B1g{B}_{1g}B1g​ and B2g{B}_{2g}B2g​ Raman-scattering spectra of the two-dimensional square lattice Hubbard model at intermediate interaction strengths and carrier concentrations near half filling. The calculations are based on an eight-site cluster approximation which gives access to both the zone-diagonal and zone-face portions of the Fermi surface. At low dopings, the zone-face regions exhibit a ``pseudogap,'' a suppression of the many-body density of states for energies near the Fermi surface. The pseudogap magnitude is largest near half filling and decreases smoothly with doping but as temperature is increased, the gap fills in rather than closes. The calculated response functions bear a strong qualitative resemblance to data taken in the pseudogap regime of high-Tc{T}_{c}Tc​ cuprates, strongly suggesting that the intermediate coupling Hubbard model accounts for much of the exotic behavior observed in high-Tc{T}_{c}Tc​ materials.
Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain ttt and interchain ${t}_{\ensuremath{\perp}}$ hopping amplitudes at half filling. A fixed value of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}=\ensuremath{-}{t}_{\ensuremath{\perp}}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime ${t}_{\ensuremath{\perp}}/t\ensuremath{\lesssim}0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.
The four-site "DCA" method of including intersite correlations in the dynamical mean-field theory is used to investigate the metal-insulator transition in the Hubbard model. At half-filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short-range order) than as a Mott phenomenon. Doping the gapped phase leads to a non–Fermi-liquid state with a Fermi surface only in the nodal regions and a pseudogap in the antinodal regions at lower dopings x ≲0.15 and to a Fermi-liquid phase at higher dopings.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
The recently proposed center-focused post-processing procedure [Phys. Rev. Res. 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to 8×8 in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the 4×4 cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.