Detecting the topological phases of the Kitaev model via complex network analysis

Llodrà Bisellach, Guillem (Supervisors Zambrini, Roberta; Giorgi, Gian Luca)
Master Thesis (2019)

We characterize the topological quantum phase transition on the 1D Kitaev model via complex network analysis. Weighted networks are created by means of several
two-body correlations measures, such as mutual information, concurrence and coherence, which serve to build different adjacency matrices. We also analytically calculate the energy spectrum of the system to study its critical properties and use topological arguments to justify the robustness of the phase transition. Correlations measurements are computed numerically in the ground state using two open-source Python libraries (QuTiP and OpenFermion) to implement the Kitaev model and analyze the results in the two topological phases. Complex network measures such as disparity, density and clustering, signal the quantum phase transition providinga wider approach to understand how the system approaches the critical region

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