Entanglement entropy on finitely ramified graphs

Abstract

We compute the entanglement entropy in a composite system separated by a finitely ramified boundary with the structure of a self-similar lattice graph. We derive the entropy as a function of the decimation factor which determines the spectral dimension, the latter being generically different from the topological dimension. For large decimations, the graph becomes increasingly dense, yielding a gain in the entanglement entropy which, in the asymptotically smooth limit, approaches a constant value. Conversely, a small decimation factor decreases the entanglement entropy due to a large number of spectral gaps which regulate the amount of information crossing the boundary. In line with earlier studies, we also comment on similarities with certain holographic formulations. Finally, we calculate the higher order corrections in the entanglement entropy which possess a log-periodic oscillatory behavior.

Higher-order topological Anderson insulator on the Sierpiński lattice

“…[1,2] In recent years, theoretical works concerning quantum effects on fractal lattices have been extensively studied, such as Anderson localization, [3][4][5] electronic [6,7] and optical conductivity, [8] plasmon dispersion relations, [9] and other related topics. [10][11][12][13][14] Despite being embedded in integer dimensional space, a fractal lattice is characterized by a non-integer Hausdorff dimension. [15] Due to its unique characteristics and motivated by the experimental developments, [16,17] the fractal lattices have attracted much attention in recent years.…”

Linearized spectral decimation in fractals

“…Recent developments of experimental techniques [1][2][3][4][5][6] open possibilities to study condensed-matter systems with complex geometries (for example, fractals) at the atomic level. Many theoretical and numerical works on fractals appeared recently including the studies on transport and optical properties [7][8][9][10][11], electronic localization [12][13][14][15], topology of fractals [16][17][18][19][20], appearance of flatbands [21][22][23][24], and others [25][26][27][28].…”