Solvable non-Hermitian skin effect in many-body unitary dynamics
We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact nonunitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmode...
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033041 |
| _version_ | 1797210699099799552 |
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| author | Marko Žnidarič |
| author_facet | Marko Žnidarič |
| author_sort | Marko Žnidarič |
| collection | DOAJ |
| description | We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact nonunitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes—the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective nonsymmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum. |
| first_indexed | 2024-04-24T10:14:44Z |
| format | Article |
| id | doaj.art-1c3fa712cffd4a5eb9cae5b6d0980463 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:14:44Z |
| publishDate | 2022-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1c3fa712cffd4a5eb9cae5b6d09804632024-04-12T17:22:48ZengAmerican Physical SocietyPhysical Review Research2643-15642022-07-014303304110.1103/PhysRevResearch.4.033041Solvable non-Hermitian skin effect in many-body unitary dynamicsMarko ŽnidaričWe study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving a compact nonunitary description of purity dynamics on qudits we find a sudden transition in the purity relaxation rate the origin of which is in the underlying boundary localized eigenmodes—the skin effect. We provide the full solution of the problem, being one of the simplest iterations of two-site matrices, namely, that each is a sum of only two projectors. This leads to rich dynamics influenced by the Jordan normal form of the kernel and, most importantly, a spectrum that is completely discontinuous in the thermodynamic limit. It provides a simple example of how a seemingly innocuous many-body unitary evolution can harbor interesting mathematical effects: an effective nonsymmetric Toeplitz transfer matrix description causes a phantom relaxation, such that the correct relaxation rate is not given by the matrix spectrum, but rather by its pseudospectrum.http://doi.org/10.1103/PhysRevResearch.4.033041 |
| spellingShingle | Marko Žnidarič Solvable non-Hermitian skin effect in many-body unitary dynamics Physical Review Research |
| title | Solvable non-Hermitian skin effect in many-body unitary dynamics |
| title_full | Solvable non-Hermitian skin effect in many-body unitary dynamics |
| title_fullStr | Solvable non-Hermitian skin effect in many-body unitary dynamics |
| title_full_unstemmed | Solvable non-Hermitian skin effect in many-body unitary dynamics |
| title_short | Solvable non-Hermitian skin effect in many-body unitary dynamics |
| title_sort | solvable non hermitian skin effect in many body unitary dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.4.033041 |
| work_keys_str_mv | AT markoznidaric solvablenonhermitianskineffectinmanybodyunitarydynamics |