Exceptional points, bulk-boundary correspondence, and entanglement properties for a dimerized Hatano-Nelson model with staggered potentials
Bibliographic record
Abstract
It is well known that the standard bulk-boundary correspondence does not hold for non-Hermitian systems in which also new phenomena such as exceptional points occur. Here, we study, mostly by analytical means, a paradigmatic one-dimensional non-Hermitian model with dimerization, asymmetric hopping, and imaginary staggered potentials. We present analytical solutions for the singular value and the eigensystem of this model with both open and closed boundary conditions. We explicitly demonstrate that the proper bulk-boundary correspondence is between topological winding numbers in the periodic case and singular values, not eigenvalues, in the open case. These protected singular values are connected to hidden edge modes that only become exact zero-energy eigenmodes in the semi-infinite chain limit. We also show that a nontrivial topology leads to protected eigenvalues in the entanglement spectrum. In the $\mathcal{PT}$-symmetric case, we find that the model has a previously overlooked phase where exceptional points become dense in the thermodynamic limit. This phase shows unusual hyper-ballistic transport properties with a dynamical critical exponent $z=1/2$.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".