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Conformal Quasicrystals and Holography
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Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a conformal quasicrystal, that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals, and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.
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Holographic Code Rate
Holographic codes on regular hyperbolic tilings have a code rate bounded by the tile side length divided by tile area, and for most regular tilings this bound is below one.
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