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 -