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

TL;DR

This study uses cluster dynamical mean field theory to analyze the doping-driven metal-insulator transition in the 2D Hubbard model, revealing asymmetries and pseudogap formation relevant to high-temperature superconductors.

Contribution

It provides a comparative analysis across multiple cluster sizes to identify universal features and artifacts in the doping-driven transition within the Hubbard model.

Findings

Hole doping leads to a two-stage transition with pseudogap formation.

Electron doping shows less pronounced momentum dependence and no pseudogap.

Results have implications for understanding high-$T_c$ cuprates and cluster DMFT applications.

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-$T_c$ 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 in some regions of the Fermi surface but gapless behavior in other regions. 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-$T_c$ cuprates and for the use of cluster dynamical mean field methods in wider classes of problems are discussed.