PDF version - MECO 42

Entanglement spreading and quantum relaxation
timescales with power-law decaying interactions
Irénée Frérot∗2,1 , Tommaso Roscilde3,2 , and Piero Naldesi5,4,2
2
Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon, Université de Lyon
(ENS Lyon) – ENS Lyon – 46 Alléee d’Italie, Lyon, F-69364, France, France
1
Ecole Normale Supérieure de Lyon (ENS Lyon) – École Normale Supérieure - Lyon – France
3
Institut Universitaire de France (IUF) – Institut Universitaire de France – 103 boulevard Saint-Michel,
75005 Paris, France, France
5
Dipartimento di Fisica e Astronomia, Università di Bologna – Via Irnerio 46, 40126 Bologna, Italy
4
Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (INFN, Sezione di Bologna) – Viale B.
Pichat, 6/2 40127 Bologna, Italy
Abstract
We investigate the physical mechanisms underlying the spreading of entanglement in a
quantum many-body system following an abrupt change of one of its control parameters –a
quench. In particular, we focus on extended systems where the interaction among the microscopic building blocks decays as a power-law 1 / rˆ{alpha} at long distance. The buildup
of correlations and entanglement in these systems has been studied a lot recently, mainly
in connection with the breakdown of Lieb-Robinson bounds for sufficiently small alpha, and
very paradoxical observations have been reported, for which no physical explanation has
been put forward : while long-range interactions enable distant subsystems to become essentially instantaneously correlated, the growth of entanglement entropy in a subsystem is
rather slowed down by long-range interactions. In this work, we propose a scenario resolving
this paradox. We argue that the growth of entanglement entropy is a relaxation process
involving time scales ranging from zero (for the fast modes) to infinity (for the slow modes),
corresponding to the divergency of the velocity of the fastest quasiparticles for sufficiently
long-range interactions. We support this scenario by analytical and numerical calculations
on the long-range XY spin model.
∗
Speaker
sciencesconf.org:meco42:126221