Topological phases of the Kitaev-Hubbard Model at half-filling

TL;DR

This paper investigates the phase diagram of the Kitaev-Hubbard model at half-filling, revealing four distinct phases including semi-metallic, antiferromagnetic insulator, and algebraic spin liquid, using advanced computational methods.

Contribution

It provides the first detailed phase diagram of the Kitaev-Hubbard model at weak to intermediate coupling, identifying novel phase transitions and critical points.

Findings

Identified four phases: two semi-metallic, one antiferromagnetic insulator, and one algebraic spin liquid.

Discovered a first-order transition between the antiferromagnetic insulator and the spin liquid.

All four phases converge at a single critical point.

Abstract

The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping $t$ and spin-dependent hopping $t'$. We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the $(U,t')$ plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.