Broken unitary picture of dynamics in quantum many-body scars
Bibliographic record
Abstract
Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis—Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>H</a:mi></a:math> can generically be partitioned into a set of terms <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>O</b:mi><b:mi>a</b:mi></b:msub></b:math> which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a “broken unitary” <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>U</c:mi><c:mi>s</c:mi></c:msub><c:mrow><c:mo>(</c:mo><c:mi>t</c:mi><c:mo>)</c:mo></c:mrow><c:mo>=</c:mo><c:msub><c:mo>∏</c:mo><c:mi>a</c:mi></c:msub><c:msup><c:mi>e</c:mi><c:mrow><c:mo>−</c:mo><c:mi>i</c:mi><c:msub><c:mi>O</c:mi><c:mi>a</c:mi></c:msub><c:mi>t</c:mi></c:mrow></c:msup></c:mrow></c:math>, where <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>H</d:mi><d:mo>=</d:mo><d:msub><d:mo>∑</d:mo><d:mi>a</d:mi></d:msub><d:msub><d:mi>O</d:mi><d:mi>a</d:mi></d:msub></d:mrow></d:math>, which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture—those with a finite set of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>O</e:mi><e:mi>a</e:mi></e:msub></e:math>, as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach. 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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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".