Over the last decade it has been established that a large body of information about
quantum many-body systems can be extracted from their entanglement properties. This
connection is emblematic concerning bipartite entanglement (either two-site or two-block
as in the entanglement entropy), both at thermal equilibrium and in the non-equilibrium
case. When it comes to multipartite entanglement, i.e. entanglement between multiple, M
> 2, subsystems, the quantification and classification is fairly much complex and the
overall picture is far less clear. Nonetheless, multipartite entanglement has proved to be a
crucial concept in understanding the collective behavior of many body systems and very
promising studies have been performed at thermal equilibrium.
Here, we present the first study of multipartite entanglement out-of-equilibium . We
quantify it through the quantum Fisher information (QFI) density. At thermal equilibrium
QFI, thanks to a connection with a dynamical susceptibility , is a very appealing
quantity because it shows critical scaling at a quantum phase transition and it makes
multipartite entanglement relatively easy to measure.
We study the QFI density of a quantum many-body system within the well-known protocol
of a quantum quench. We are able to express it in terms of a generalised response
function. For pure state initial conditions and in the thermodynamic limit, we can express
the QFI as the fluctuations of an observable computed in the so-called diagonal ensemble.
We apply our formalism to the dynamics of a quantum Ising chain, quenching the
transverse field. We find that in this model the asymptotic state is always multipartite
entangled. More interestingly, for quenches within the ferromagnetic phase, we find a
divergence of multipartite entanglement emerging in the asymptotic state by performing
“small quenches”; this behavior is connected to a corresponding divergence of the
correlation length of the order parameter.
1. S. Pappalardi, A. Russomanno, A. Silva, R. Fazio, in press on JSTAT, (2017).
2. P. Hauke, M. Heyl, L. Tagliacozzo, and P. Zoller, Nat. Phys. 12, 778 (2016).