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

• URL: http://arxiv.org/abs/2401.05954v2
• Date: Sun, 30 Jun 2024 22:25:14 GMT
• Title: Structure and scaling of Kitaev chain across a quantum critical point in real space
• Authors: Yan He, Chih-Chun Chien,
• Abstract summary: The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with inhomogeneous pairing interactions. The BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region. The Bogoliubov-de Gennes equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime.
• Score: 1.4206639868377509
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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