Free fermions with dephasing and boundary driving: Bethe Ansatz results
By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe Ansatz to diagonalize the Liouvillian $\mathcal{L}^{(2)}$ governing the dynamics of the correlator. The major...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-01-01
|
| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.8.1.011 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832578888965816320 |
|---|---|
| author | Vincenzo Alba |
| author_facet | Vincenzo Alba |
| author_sort | Vincenzo Alba |
| collection | DOAJ |
| description | By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe Ansatz to diagonalize the Liouvillian $\mathcal{L}^{(2)}$ governing the dynamics of the correlator. The majority of its eigenvalues are complex. Precisely, $L(L-1)/2$ complex eigenvalues do not depend on dephasing, apart from a trivial shift. The remaining complex levels are perturbatively related to the dephasing-independent ones for large $L$. The long-time dynamics is governed by a band of real eigenvalues, which contains an extensive number of levels. They give rise to diffusive scaling at intermediate times, when boundaries can be neglected. Moreover, they encode the breaking of diffusion at asymptotically long times. Interestingly, for large loss rate two boundary modes appear in the spectrum. The real eigenvalues correspond to string solutions of the Bethe equations, and can be treated effectively for large chains. This allows us to derive compact formulas for the dynamics of the fermionic density. We check our results against exact diagonalization, finding perfect agreement. |
| format | Article |
| id | doaj-art-488c80be64ff4f77a8341c3d89e77573 |
| institution | Kabale University |
| issn | 2666-9366 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj-art-488c80be64ff4f77a8341c3d89e775732025-01-30T13:22:53ZengSciPostSciPost Physics Core2666-93662025-01-018101110.21468/SciPostPhysCore.8.1.011Free fermions with dephasing and boundary driving: Bethe Ansatz resultsVincenzo AlbaBy employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe Ansatz to diagonalize the Liouvillian $\mathcal{L}^{(2)}$ governing the dynamics of the correlator. The majority of its eigenvalues are complex. Precisely, $L(L-1)/2$ complex eigenvalues do not depend on dephasing, apart from a trivial shift. The remaining complex levels are perturbatively related to the dephasing-independent ones for large $L$. The long-time dynamics is governed by a band of real eigenvalues, which contains an extensive number of levels. They give rise to diffusive scaling at intermediate times, when boundaries can be neglected. Moreover, they encode the breaking of diffusion at asymptotically long times. Interestingly, for large loss rate two boundary modes appear in the spectrum. The real eigenvalues correspond to string solutions of the Bethe equations, and can be treated effectively for large chains. This allows us to derive compact formulas for the dynamics of the fermionic density. We check our results against exact diagonalization, finding perfect agreement.https://scipost.org/SciPostPhysCore.8.1.011 |
| spellingShingle | Vincenzo Alba Free fermions with dephasing and boundary driving: Bethe Ansatz results SciPost Physics Core |
| title | Free fermions with dephasing and boundary driving: Bethe Ansatz results |
| title_full | Free fermions with dephasing and boundary driving: Bethe Ansatz results |
| title_fullStr | Free fermions with dephasing and boundary driving: Bethe Ansatz results |
| title_full_unstemmed | Free fermions with dephasing and boundary driving: Bethe Ansatz results |
| title_short | Free fermions with dephasing and boundary driving: Bethe Ansatz results |
| title_sort | free fermions with dephasing and boundary driving bethe ansatz results |
| url | https://scipost.org/SciPostPhysCore.8.1.011 |
| work_keys_str_mv | AT vincenzoalba freefermionswithdephasingandboundarydrivingbetheansatzresults |