Entanglement entropy of highly degenerate states and fractal dimensions

Details Entanglement entropy of highly degenerate states and fractal dimensions Entanglement entropy of highly degenerate states and fractal dimensions

2011-03-16

arxiv.org/abs/1103.3247v1

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

We consider the bi-partite entanglement entropy of ground states of extended quantum systems with a large degeneracy due to a spontaneously broken global Lie group symmetry. In general, a ground state is a linear combination of basis elements of a representation space, and for extended systems, these basis elements form a manifold. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges logarithmically as (d/2) log m, where d is the fractal dimension of the sub-variety of the manifold of basis elements occurring in the linear combination. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds in general for largely degenerate ground states, with potential applications to quenched disorder.

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