Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model

Abstract

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 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 cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.

Continuous-pole-expansion method to obtain spectra of electronic lattice models

“…First we use the CPE to investigate the momentum dependence of the spectrum in the single-band Hubbard model in two dimensions at half-filling. Particularly the momentum dependence of the gap formation has received a lot of interest recently [25,27], and there are several results in the literature to compare to. We can further validate the CPE by looking at the K-dependent self-energy obtained from quantum Monte Carlo simulations within the DCA.…”

“…Recently, much attention has been given to the momentum-dependent gap formation at half-filling in the single-band Hubbard model. In particular, it has been shown [25,27] that for a specific interaction strength of U/t = 6, the antinodal regions ([±π,0] and [0, ± π ]) lose their spectral weight contribution at the Fermi energy faster than the nodal regions ([±π/2, ± π/2]). This momentum anisotropy in the self-energy is a very interesting phenomenon since exotic ground states, such as the antiferromagnetic and d-wave superconducting state require a momentum-dependent self-energy.…”

“…Furthermore, we can immediately observe that this anisotropy in the self-energy increases as the temperature T is lowered. Using the partial occupancies n K in the different patches of the Brillouin zone, Gull et al [27] have claimed that the gap opened at the nodal region should be much bigger than at the antinodal region. Defining the width of the gap as the minimum distance between the two van Hove singularities in Fig.…”

“…We illustrate how the CPE can be used to inspect the momentum dependence of the spectrum by investigating the momentum-dependent gap formation. This topic has been recently investigated on small clusters [25][26][27], but without any conclusions on the spectral functions. We will show that the CPE arrives at the same conclusions as in the literature and investigate the spectral functions more closely.…”

“…Since DMFT introduces correlations that have already been partly accounted for in the LDA functional, a double-counting correction H dc needs to be applied to our impurity Hamiltonian H in Eq. (27). For this we follow the standard procedure of Karolak et al [42].…”