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arXiv:0909.1795 · Physical Review B

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

Emanuel Gull, Olivier Parcollet, Philipp Werner, Andrew J. Millis

Published Dec 1, 2009• 112 citations
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Abstract

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.

DOI
10.1103/physrevb.80.245102

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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 (\ensuremathπ,\ensuremathπ)(\ensuremath{\pi},\ensuremath{\pi})(\ensuremathπ,\ensuremathπ) but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.
Metal-insulator transitions in the paramagnetic phase of the two-dimensional square-lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transitions are multistage and momentum-sector specific with Fermi-liquid metal and fully gapped insulator phases separated by an intermediate phase, in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.
Metal-insulator transitions in the paramagnetic phase of the two-dimensional square-lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transitions are multistage and momentum-sector specific with Fermiliquid metal and fully gapped insulator phases separated by an intermediate phase, in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarsegrained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.
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.
Cluster dynamical mean-field calculations based on 2-, 4-, 8-, and 16-site clusters are used to analyze the doping-driven metal-insulator transition in the two-dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole-doped side than on the electron-doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-Tc{T}_{c}Tc​ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi-liquid renormalizations are larger and the electron self-energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap on some parts of the Fermi surface but gapless behavior in other parts. On the electron-doped side the partially gapped regime does not occur, and the momentum dependence of the electron self-energy is less pronounced. Implications for the high-Tc{T}_{c}Tc​ cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.
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.
We introduce a Cellular Dynamical Cluster Approximation (CDCA) to study the nature of the Mott insulator-metal transition in the extended Hubbard model on a square lattice. At strong coupling, a d-wave Mott insulator is obtained. Hole doping drives a first order Mott transition to a non-Fermi (nFL) liquid metal. Remarkably, this nFL is caused by an Anderson orthogonality catastrophe at low energies due to the non-trivial competition between strong, non-local interactions and hopping. This constitutes the first explicit realisation of Anderson's Luttinger liquid idea in two dimensions. Many experimental responses in the ``strange metal'' phase found around optimal doping in cuprates are understood naturally within our approach.