Quantum information approach to the quantum phase transition in the Kitaev honeycomb model

Abstract

Kitaev honeycomb model with topological phase transition at zero temperature is studied using quantum information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with longest distance are obtained. It is found that the mutual information show some singularities at the critical point where the ground state of the system transits from gapless phase to gapped phase. The finite-size effects and scalar behavior are also studied. The mutual information can serve as good indicators of the topological phase transition, since the mutual information catches some global correlation properties of the system. Meanwhile, this method has other advantages such that the phase transition can be determined easily and the order parameters are not required previously, for the order parameters of some topological phase transitions are hard to know.

8 pages, 7 figures, published version

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• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Quantum correlations and entanglement in a Kitaev-type spin chain
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Compass and Kitaev models -- Theory and Physical Motivations
• Revealing divergent length scales using quantum Fisher information in the Kitaev honeycomb model
• Entanglement-assisted local operations and classical communications conversion in the quantum critical systems
• Cumulative measure of correlation for multipartite quantum states
• Majorization relation in quantum critical systems
• Phase diagram of quantum critical system via local convertibility of ground state
• Probing phase transitions in non-Hermitian systems with quantum entanglement