Quantum phase transitions in the Kitaev model on decorated lattices

Abstract

We have proposed an exactly solvable model defined on 2D decorated lattices of two types. The ground-state phase diagram of the system includes different topological phases with gapless chiral edge states. We show that two types of chiral spin liquid with gapless edge modes are realized on lattices with different symmetry. The phase transition between the topological phase with chiral gapped (Chern number zero) and the topological phase with chiral gapless edge modes (Chern number ) occurs in the model on the square (symmetric) decorated lattice. On the rectangular (asymmetric) decorated lattice the topological phase is defined by a chiral gapless (gapped) edge mode in the x (y) direction and a chiral gapped (gapless) edge mode in another y (x) direction. We show that a Kitaev model on a decorated asymmetric square lattice exhibits the quantum phase transition between topological phases with equal Chern numbers.