# Sublogarithmic behaviour of the entanglement entropy in fermionic chains

## TL;DR

This paper investigates the entanglement entropy in long-range quantum chains, revealing sublogarithmic growth under certain conditions, based on analyzing Toeplitz determinants outside traditional theoretical frameworks.

## Contribution

It introduces a novel analysis of Toeplitz determinants with non-standard symbols to explain sublogarithmic entanglement entropy growth in long-range Kitaev chains.

## Key findings

- Entanglement entropy can grow sublogarithmically in certain long-range quantum systems.
- New class of Toeplitz determinants analyzed beyond classical theorems.
- Results suggest alternative behaviors of quantum entanglement in extended systems.

## Abstract

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szeg\H{o} Theorem or the Fisher-Hartwig conjecture.