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arXiv · 1511.01330

Entangling Fractals

Amin Faraji Astaneh
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Abstract

We use the Heat Kernel method to calculate the Entanglement Entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cut-off parameter is (generally) a fractional number which indeed is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel $\log$ periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the Holographic calculation in a certain hyper-scaling violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyper-scaling violating theory with the spectral dimension of the fractal. We provide more supports with comparing the behavior of the thermal entropy in terms of the temperature computed for a fractal geometry and a hyper-scaling violating theory as well.

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Amin Faraji Astaneh. 2015-11-08. Entangling Fractals. https://doi.org/10.1103/physrevd.93.066004

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