Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2307.03107 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913247255330816 |
|---|---|
| author | Tang, Yin Zhu, W. |
| author_facet | Tang, Yin Zhu, W. |
| contents | Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03107 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix Tang, Yin Zhu, W. Quantum Physics Strongly Correlated Electrons Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian systems, while the possible non-Hermitian solution remains outstanding. In this work, we generalize the quantum covariance matrix method to the cases that are applicable to non-Hermitian systems, through which we are able to explicitly reconstruct the non-Hermitian parent Hamiltonian from an arbitrary pair of biorthogonal eigenstates. As concrete examples, we successfully apply our approach in spin chain with Lee-Yang singularity and a non-Hermitian interacting fermion model. Some generalization and further application of our approach are also discussed. Our work provides a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates and shed light on future exploration on non-Hermitian physics. |
| title | Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.03107 |