FisMat2017 - Submission - View

Abstract's title: Multipartite entanglement after a quantum quench
Submitting author: Silvia Pappalardi
Affiliation: SISSA, ICTP
Affiliation Address: Via Bonomea, 265, 34136 Trieste
Country: Italy
Oral presentation/Poster (Author's request): Poster
Other authors and affiliations: Angelo Russomanno (3, 1), Alessandro Silva (2), Rosario Fazio (1, 3) 1 Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy 2 SISSA, Via Bonomea 265, I-34135 Trieste, Italy 3 NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
Abstract

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 [1]. We

quantify it through the quantum Fisher information (QFI) density. At thermal equilibrium

QFI, thanks to a connection with a dynamical susceptibility [2], 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.

References

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).