Topological properties of single-particle states decaying into a continuum due to interaction
Bibliographic record
Abstract
We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>H</a:mi> <a:mn>0</a:mn> </a:msub> </a:math> corrected by the self-energy <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi mathvariant="normal">Σ</b:mi> </b:math> to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mrow> <d:msub> <d:mi>H</d:mi> <d:mtext>eff</d:mtext> </d:msub> <d:mo>=</d:mo> </d:mrow> <d:msub> <d:mi>H</d:mi> <d:mn>0</d:mn> </d:msub> <d:mrow> <d:mo>(</d:mo> <d:mover accent="true"> <d:mi>k</d:mi> <d:mo>⃗</d:mo> </d:mover> <d:mo>)</d:mo> </d:mrow> <d:mo>+</d:mo> <d:mi mathvariant="normal">Σ</d:mi> <d:mrow> <d:mo>(</d:mo> <d:mi>ω</d:mi> <d:mo>,</d:mo> <d:mover accent="true"> <d:mi>k</d:mi> <d:mo>⃗</d:mo> </d:mover> <d:mo>)</d:mo> </d:mrow> </d:mrow> </d:math> reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msub> <h:mi>H</h:mi> <h:mtext>eff</h:mtext> </h:msub> </h:math> and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize. Published by the American Physical Society 2024
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".