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 = – 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

 


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

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

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