Structure and scaling of Kitaev chain across a quantum critical point in real space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910542578319360 |
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| author | He, Yan Chien, Chih-Chun |
| author_facet | He, Yan Chien, Chih-Chun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure and scaling of Kitaev chain across a quantum critical point in real space He, Yan Chien, Chih-Chun Superconductivity Strongly Correlated Electrons Quantum Physics 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. |
| title | Structure and scaling of Kitaev chain across a quantum critical point in real space |
| topic | Superconductivity Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2401.05954 |