Symmetry protected exceptional points of interacting fermions
Non-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a nondiagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigat...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-09-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033181 |
| _version_ | 1797210688469336064 |
|---|---|
| author | Robin Schäfer Jan C. Budich David J. Luitz |
| author_facet | Robin Schäfer Jan C. Budich David J. Luitz |
| author_sort | Robin Schäfer |
| collection | DOAJ |
| description | Non-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a nondiagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional “fans.” In addition, (ii) we identify a new source for exceptional points which are only present due to the interaction. These points emerge from diagonalizable degeneracies in the noninteracting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint. These phenomena are well captured by an “exceptional perturbation theory” starting from a noninteracting Hamiltonian. |
| first_indexed | 2024-04-24T10:14:34Z |
| format | Article |
| id | doaj.art-fd87c84f332d4517ab46429e1c6bb1c4 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:14:34Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-fd87c84f332d4517ab46429e1c6bb1c42024-04-12T17:24:13ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-014303318110.1103/PhysRevResearch.4.033181Symmetry protected exceptional points of interacting fermionsRobin SchäferJan C. BudichDavid J. LuitzNon-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a nondiagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional “fans.” In addition, (ii) we identify a new source for exceptional points which are only present due to the interaction. These points emerge from diagonalizable degeneracies in the noninteracting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third order exceptional point at the endpoint. These phenomena are well captured by an “exceptional perturbation theory” starting from a noninteracting Hamiltonian.http://doi.org/10.1103/PhysRevResearch.4.033181 |
| spellingShingle | Robin Schäfer Jan C. Budich David J. Luitz Symmetry protected exceptional points of interacting fermions Physical Review Research |
| title | Symmetry protected exceptional points of interacting fermions |
| title_full | Symmetry protected exceptional points of interacting fermions |
| title_fullStr | Symmetry protected exceptional points of interacting fermions |
| title_full_unstemmed | Symmetry protected exceptional points of interacting fermions |
| title_short | Symmetry protected exceptional points of interacting fermions |
| title_sort | symmetry protected exceptional points of interacting fermions |
| url | http://doi.org/10.1103/PhysRevResearch.4.033181 |
| work_keys_str_mv | AT robinschafer symmetryprotectedexceptionalpointsofinteractingfermions AT jancbudich symmetryprotectedexceptionalpointsofinteractingfermions AT davidjluitz symmetryprotectedexceptionalpointsofinteractingfermions |