Details
| Original language | English |
|---|---|
| Article number | 205107 |
| Journal | Physical Review B |
| Volume | 101 |
| Issue number | 20 |
| Publication status | Published - 15 May 2020 |
| Externally published | Yes |
Abstract
We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) "quantum many-body scars": energy eigenstates with energies placed in an equally spaced ladder and with Rényi entanglement entropy of at most O(log(N))+O(|∂A|) for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Condensed Matter Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Physical Review B, Vol. 101, No. 20, 205107, 15.05.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Revivals imply quantum many-body scars
AU - Alhambra, Álvaro M.
AU - Anshu, Anurag
AU - Wilming, Henrik
N1 - Funding Information: The authors acknowledge useful discussions with Cheng-Ju Lin. H.W. acknowledges support from the Swiss National Science Foundation through SNSF Project No. 200020_165843 and through the National Centre of Competence in Research Quantum Science and Technology (QSIT). A.A. is supported by the Canadian Institute for Advanced Research, through funding provided to the Institute for Quantum Computing by the Government of Canada and the Province of Ontario. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.
PY - 2020/5/15
Y1 - 2020/5/15
N2 - We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) "quantum many-body scars": energy eigenstates with energies placed in an equally spaced ladder and with Rényi entanglement entropy of at most O(log(N))+O(|∂A|) for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.
AB - We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) "quantum many-body scars": energy eigenstates with energies placed in an equally spaced ladder and with Rényi entanglement entropy of at most O(log(N))+O(|∂A|) for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.
UR - http://www.scopus.com/inward/record.url?scp=85085843322&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.101.205107
DO - 10.1103/PhysRevB.101.205107
M3 - Article
AN - SCOPUS:85085843322
VL - 101
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 20
M1 - 205107
ER -