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arXiv · 2401.05954

Structure and scaling of Kitaev chain across a quantum critical point in real space

Yan He·Chih-Chun Chien
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Abstract

The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov-de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench shows the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states.

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Yan He, Chih-Chun Chien. 2024-01-11. Structure and scaling of Kitaev chain across a quantum critical point in real space. https://doi.org/10.1088/1361-648x%2Fad64a0

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