Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes

TL;DR

This paper analyzes the entanglement entropy scaling in free fermions on folded cubes, showing it strictly follows the area law without the expected logarithmic enhancement, using algebraic decomposition methods.

Contribution

It provides an analytical derivation of entanglement scaling on folded cubes and explains the absence of logarithmic enhancement through algebraic decomposition.

Findings

Entanglement entropy obeys the area law without logarithmic enhancement.

Analytical expression derived in the large-diameter limit.

Decomposition based on Terwilliger algebra explains the observed behavior.

Abstract

This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-diameter limit, revealing a strict adherence to the area law. The absence of the logarithmic enhancement expected for free fermions is explained using a decomposition of folded cubes in chains based on its Terwilliger algebra and $\mathfrak{so}(3)_{-1}$. The entanglement Hamiltonian and its relation to Heun operators are also investigated.