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arXiv:0805.3778 · Europhysics Letters (EPL)

Local order and the gapped phase of the Hubbard model: A plaquette dynamical mean-field investigation

Emanuel Gull, Philipp Werner, Xin Wang, Matthias Troyer, Andrew J. Millis

Published Oct 29, 2008• 103 citations
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Abstract

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.

DOI
10.1209/0295-5075/84/37009

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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.
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.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.
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.
A powerful diagrammatic impurity solver is shown to permit a systematic study of the doping-driven Mott transition in a one-band Hubbard model within the framework of single-site dynamical mean-field theory. At small dopings and large interaction strengths, we are able to access low enough temperatures that a reliable extrapolation to temperature T=0T=0T=0 may be performed, and ground state energies of insulating and metallic states may be compared. We find that the T=0T=0T=0 doping-driven transition is of second order and is characterized by an interaction-strength dependent electronic compressibility, which vanishes at the critical interaction strength of the half filled model. Over wide parameter ranges, the compressibility is substantially reduced relative to the noninteracting system. The metal-insulator transition is characterized by the appearance of in-gap states, but these are relevant only for very low dopings of less than 3%.
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.