Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909303803215872 |
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| author | Sinha, Akash Ghosh, Aritra Bagchi, Bijan |
| author_facet | Sinha, Akash Ghosh, Aritra Bagchi, Bijan |
| contents | Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator Sinha, Akash Ghosh, Aritra Bagchi, Bijan Quantum Physics High Energy Physics - Theory Mathematical Physics Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases. |
| title | Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2401.17189 |