1. Quantum phase transitions in Kitaev spin models
Xiao-Feng Shi, Yan Chen, and J. Q. You
Department of Physics and Surface Physics Laboratory, Fudan University, Shanghai, , China
We study the quantum phase transitions in the Kitaev spin models on both honeycomb and Fisher (triangle-honeycomb) lattices. Our analytical results show that the Kitaev spin model on the honeycomb lattice exhibits a continuous quantum phase transition. We also reveal the relationship between bipartite entanglement and the ground-state energy. Our approach directly shows that both the entanglement and the ground-state energy can be used to characterize the topological quantum phase transition in the Kitaev spin model on the honeycomb lattice. Also, we show that the quantum phase transitions can occur in the same topological class for the Kitaev spin model on a Fisher lattice.
I. Extended Kitaev spin model on a honeycomb lattice
IV. Relation between the nonanalyticity of the ground-state energy and that of the bipartite entanglement
Hamiltonian:
where
V. Quantum phase transitions in the Kitaev spin model on a Fisher (triangle-honeycomb) lattice
Hamiltonian:
II. Ground-state energy and its derivatives
Left: Phase diagram of the extended Kitaev model. The gray region corresponds to the non-Abelian phase, and the three triangular regions correspond to the Abelian phase.
Phase diagram : Case 1
Left: Phase diagram. The yellow (red) regions are phases of Chern number 1 (-1). The white regions are phases of Chern number 0.
Right: A first-order quantum phase transition occurring along the horizontal dashed line.
III. Bipartite entanglement and its derivatives
Phase diagram : Case 2
Left: Phase diagram. The yellow (red) regions are phases of Chern number 1 (-1). The white regions are phases of Chern number 0.
Right: a continuous quantum phase transition occurring along the dashed line.
VI. Conclusions
A continuous QPT occurs on the critical lines separating the Abelian and non-Abelian phases in the Kitaev model on a honeycomb lattice. Our approach shows that both the entanglement and the ground-state energy can be used to characterize the topological quantum phase transition in the Kitaev spin model on the honeycomb lattice.
We show that the quantum phase transitions can occur in the same topological class for the Kitaev spin model on a Fisher lattice.