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Revivals imply quantum many body scars
Alvaro Alhambra - Perimeter Institute
Wednesday, February 26, 2020, 11:00 am-12:15 pm Calendar
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We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a 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 at most poly(N) implies the existence of "quantum many-body scars", whose number grows at least as the square root of N up to poly-logarithmic factors. These are energy eigenstates with energies placed in an equally-spaced ladder and with Rényi entanglement entropy scaling as log(N), plus an area law term for any region of the lattice. This shows that quantum many-body scars are a necessary condition for revivals, independent of particularities of the Hamiltonian leading to them, and helps explain their appearance in a number of recently found ergodicity-breaking models. We also present results for approximate revivals and for revivals of expectation values of observables.  Joint work with Henrik Wilming and Anurag Anshu

This talk is organized by Andrea F. Svejda