Entanglement Entropy in Ground States of Long-Range Fermionic Systems

TL;DR

This paper investigates how the entanglement entropy in ground states of long-range fermionic systems scales with the decay exponent, revealing a transition from area-law to volume-law behavior influenced by system disorder and continuum limits.

Contribution

It provides a numerical and theoretical analysis of entanglement entropy scaling in long-range fermionic models, identifying conditions for different scaling regimes and the impact of disorder.

Findings

Entanglement entropy transitions from area-law to volume-law as decay exponent decreases.

Scaling is constrained by low-energy continuum theory in applicable models.

Disordered and non-continuum models exhibit fractal and volume-law scaling near zero decay exponent.

Abstract

We study the scaling of ground state entanglement entropy of various free fermionic models on one dimensional lattices, where the hopping and pairing terms decay as a power law. We seek to understand the scaling of entanglement entropy in generic models as the exponent of the power law $\alpha$ is varied. We ask if there exists a common $\alpha_{c}$ across different systems governing the transition to area law scaling found in local systems. We explore several examples numerically and argue that when applicable, the scaling of entanglement entropy in long-range models is constrained by predictions from the low-energy theory. In contrast, disordered models and models without a continuum limit show fractal scaling of entanglement approaching volume-law behavior as $\alpha$ approaches zero. These general features are expected to persist on turning on interactions.