# Séminaire du LPTMS: Grégoire Misguich

## 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 = – Σ_{i} 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

**Date/Time : ** 25/04/2017 - *11:00 - 12:00*

**Location : ** LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

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