Download Quantum phase transitions in Kitaev spin models

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, 200433, 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.
IV. Relation between the nonanalyticity of the ground-state
energy and that of the bipartite entanglement
I. Extended Kitaev spin model on a honeycomb lattice
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
2
Left: Phase diagram of
the extended Kitaev
model. The gray region
corresponds to the nonAbelian 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
1. A continuous QPT occurs on the critical lines separating the Abelian and nonAbelian 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.
2. We show that the quantum phase transitions can occur in the same topological
class for the Kitaev spin model on a Fisher lattice.