Next seminar : Séminaire du LPTMS: Grégoire Misguich

Tuesday, April 25 2017 at 11:00:00

Entanglement and Shannon entropies in low dimensional magnets

Grégoire Misguich (IPhT, CEA, Saclay)

The entanglement (von Neumann) entropy is now routinely used by condensed-matter theorists as a tool to probe quantum many-body  systems, since it often gives access to properties that are not easily visible using more conventional observables. I will illustrate this using a few examples taken from the literature on 1D and 2D spin systems. I will then discuss a related but different entropy, the Shannon entropy, which can also be used as a tool to probe many-body  systems. The Shannon entropy of a many-body state |ψ>  is defined by expanding the wave-function in some preferential configuration basis { |i> }. The projections of  |ψ> onto the basis states define a set of normalized probabilities p[i] = |<ψ|i>|2, and these probabilities can used to define an associated Shannon entropy S = - Σi p[i]*log(p[i]). This quantity measures hos 'localized" is |ψ>, in the chosen basis. While the entanglement entropy requires the choice of a specific subsystem, the Shannon entropies is basis-dependent but is defined for the system as a whole. In this talk we discuss a few examples in 1D and 2D where some universal information about the long-distance physics of the system can be obtained by analyzing the scaling of S as a function of the system size. In particular, we show that the spontaneous symmetry breaking of a continuous symmetry (as in Néel-ordered antiferromagnets) leads in 2D to some universal logarithmic terms in the Shannon entropy Reference:
  • G. Misguich, V. Pasquier & M. Oshikawa, Shannon-Rényi entropy for Nambu-Goldstone modes in two dimensions, preprint arXiv:1607.02465
 

Last Highlight : Geometry and interactions in self-assembled biological systems

In honour of Françoise Livolant, the LPS (Laboratoire de Physique des Solides) and LPTMS (Laboratoire de Physique Théorique et Modèles Statistiques) are organising an international conference on geometry and interactions in self-assembled biological systems.

We will host a two days conference in Orsay, on March 23-24, 2017. Colleagues and friends are welcome.

Participants may submit their contributions to poster sessions.

Registration is free of charge but mandatory.

The conference will be held at the Institut de Physique Nucléaire (IPN), Orsay (Building 100A), close to the train station Orsay Ville on the RER B line.

The link of the conference: https://flivolant2017.sciencesconf.org/


See all LPTMS highlights.


Next Conference :