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

TL;DR

This study investigates momentum-sector-selective metal-insulator transitions in a two-dimensional Hubbard model using an eight-site dynamical mean-field approximation, revealing phase diagram details and transition orders.

Contribution

It provides the first detailed phase diagram for sector-selective transitions in this model and clarifies the nature of these transitions and their relation to spin correlations.

Findings

Second-order transitions involve continuous energy gap opening.

Non-Fermi-liquid behavior in ungapped Fermi surface regions.

Transitions are not caused by Van Hove singularities.

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 $(\pi,\pi)$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.