  We examine the existence of the interaction-generated quantum anomalous Hall
phase on the honeycomb lattice. For the spinless model at half filling, the
existence of a quantum anomalous Hall phase (Chern insulator phase) has been
predicted using mean-field methods. However, recent exact diagonalization
studies for small clusters with periodic boundary condition have not found a
clear sign of an interaction-driven Chern insulator phase. We use exact
diagonalization method to study properties of small clusters with open boundary
condition and, contrary to previous studies, we find clear signatures of the
topological phase transition for finite size clusters. We also examine
applicability of the entangled-plaquette state (correlator-product state)
ansatz to describe the ground states of the system. Within this approach the
lattice is covered with plaquettes and the ground state wave-function is
written in terms of the plaquette coefficients. Configurational weights can
then be optimized using a variational Monte Carlo algorithm. Using the
entangled-plaquette state ansatz we study the ground state properties of the
system for larger system sizes and show that the results agree with the exact
diagonalization results for small clusters. This confirms validity of the
entangled-plaquette state ansatz to describe the ground states of the system
and provides further confirmation of the existence of the quantum anomalous
Hall phase in the thermodynamic limit, as predicted by the mean-field theory
calculations.
