RECORD
Conserved Quantities from Entanglement Hamiltonian
Statistical Mechanics · Submitted 23 Apr 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is cut off around the order of subregion volume, and some of their EHSM eigen-operators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly in power law if the system is integrable, with the exponent $s\approx 1$ ($s\approx 1.5\sim 2$) if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigen-operators of which correspond to the identity and the subregion Hamiltonian.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. | result 0.94 | 0.93 | 0.85 | asserted 1.00 |
| s1 | By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. | method 0.96 | 0.83 | 0.09 | asserted 0.78 |
| s2 | For free fermions, we find the number of nonzero EHSM eigenvalues is cut off around the order of subregion volume, and some of their EHSM eigen-operators can be rather nonlocal, although subregionally quasilocal. | result 1.00 | 0.95 | 0.06 | asserted 1.00 |
| s3 | In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly in power law if the system is integrable, with the exponent $s\approx 1$ ($s\approx 1.5\sim 2$) if the eigenstates are extended (many-body localized). | result 1.00 | 0.95 | 0.07 | asserted 1.00 |
| s4 | For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigen-operators of which correspond to the identity and the subregion Hamiltonian. | result 1.00 | 0.89 | 0.13 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is cut off around the order of subregion volume, and some of their EHSM eigen-operators can be rather nonlocal, although subregionally quasilocal. In the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues decay roughly in power law if the system is integrable, with the exponent $s\approx 1$ ($s\approx 1.5\sim 2$) if the eigenstates are extended (many-body localized). For fully chaotic systems, only two EHSM eigenvalues are significantly nonzero, the eigen-operators of which correspond to the identity and the subregion Hamiltonian.
Human review
References
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 1 sentence without a confident label
Cites as background 4 papers
-
This, however, usually requires certain large flavor limit, for instance in the Sachdev-Ye-Kitaev type models [ref] .
The Spectrum in the Sachdev-Ye-Kitaev Model · Introduction · 0.81
-
This, however, usually requires certain large flavor limit, for instance in the Sachdev-Ye-Kitaev type models [ref] .
Comments on the Sachdev-Ye-Kitaev model · Introduction · 0.81
-
This, however, usually requires certain large flavor limit, for instance in the Sachdev-Ye-Kitaev type models [ref] .
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual · Introduction · 0.81
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.