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Entanglement Entropy of Highly Degenerate States and Fractal Dimensions

Castro-Alvaredo, O. & Doyon, B. (2012). Entanglement Entropy of Highly Degenerate States and Fractal Dimensions. Physical Review Letters (PRL), 108(12), doi: 10.1103/PhysRevLett.108.120401


We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. 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 as d/2log⁡m, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. 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 quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.

Publication Type: Article
Additional Information: © 2012 American Physical Society
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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