Topological quantum phase transition in the extended Kitaev spin model

Abstract

We study the quantum phase transition between Abelian and non-Abelian phases in an extended Kitaev spin model on the honeycomb lattice, where the periodic boundary condition is applied by placing the lattice on a torus. Our analytical results show that this spin model exhibits a continuous quantum phase transition. Also, we 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 extended Kitaev spin model.

Quantum Fisher information as a signature of the superradiant quantum phase transition

“…In figure 3(a), we confirm that the degree of squeezing Δˆ< π X 4( ) 1 /2 2 , and that it is minimized at λ λ ∼ cr for large enough N. Similarly, one can consider the spin squeezing of the atomic state ρ A . Due to the conserved parity, the atoms have vanishing coherence 〈ˆ〉 = + J 0 and hence the total spin 〈ˆ〉 = 〈ˆ〉 J J (0, 0, ) z , similar to that of the Lipkin-Meshkov-Glick model [4][5][6]12]. To quantify the degree of spin squeezing [43][44][45][46][47][48][49], one can introduce a spin component…”

“…In the thermodynamic limit, we present the analytical results of the QFI and their relationship with the reduced variances of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.Quantum phase transitions in many-body systems are of fundamental interest [1] and have potential applications in quantum information [2][3][4][5][6][7] and quantum metrology [8][9][10][11][12][13][14][15]. Consider, for instance, a collection of N two-level atoms interacting with a single-mode bosonic field, described by the Dicke model (with =  1) [16]:z 0 whereb andˆ † b are annihilation and creation operators of the bosonic field with oscillation frequency ω, which is nearly resonant with the atomic energy splitting ω 0 .…”

Exotic phase diagram of a topological quantum system

“…[2][3][4][5] Because the ground states in some topological quantum systems (e.g., the Kitaev spin models on honeycomb 3 and triangle-honeycomb 5 lattices) are exactly solvable, QPTs in these systems can be analytically investigated. In these topological systems, the discovered QPTs include the transition between a gapped Abelian phase and a gapless phase, 4,6 the transition between Abelian and non-Abelian phases, 5,[7][8][9][10] and the transition between two non-Abelian phases with different Chern numbers. 3 Also, an unconventional QPT between two non-Abelian phases was found 11 in the Kitaev spin model on a trianglehoneycomb lattice by a fermionization method.…”

Quantum phase transition of the one-dimensional transverse-field compass model

“…It is exactly the same as the 1D reduced Kitave model. [11][12][13][14] The symmetry of the pseudospin Hamiltonian is much lower than SU͑2͒. It is shown in the numerical results that the eigenstates are at least twofold degenerate or highly degenerate.…”