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.

Highlights

  • Entanglement is one of the most intriguing features of the physical world. It lays the foundation of quantum information theory as well as other branches of physics such as quantum computing and cryptography [1,2,3]. It has an important role in condensed matter physics, in strongly correlated systems [4,5], the latter providing a natural ground for the emergence of collective quantum phenomena

  • We study the entanglement entropy in a composite system with a separating boundary finitely ramified in form of a self-similar lattice graph

  • We have found that increasing the topological decimation factor leads to an increase in the Entanglement entropy (EE)

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Summary

INTRODUCTION

Entanglement is one of the most intriguing features of the physical world. It lays the foundation of quantum information theory as well as other branches of physics such as quantum computing and cryptography [1,2,3]. We study the entanglement entropy in a composite system with a separating boundary finitely ramified in form of a self-similar lattice graph. Self-similar structures, referred to as deterministic fractals, appear in various branches of physics ranging from condensed matter [26,27,28,29] to quantum field theory [30,31,32,33,34,35] They have been applied to study phase transitions in critical many body quantum systems by noticing the underlying scale invariance at the critical point [36,37,38], which has notable resemblance with the renormalization group approach [39].

ENTANGLED SUBSYSTEMS
SELF-SIMILAR RAMIFICATIONS
Leading order
Higher orders
CONCLUSION
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