Entanglement dualities in supersymmetry

TL;DR

This paper establishes a general duality relation between bosonic and fermionic entanglement in supersymmetric quadratic Hamiltonians, revealing a phenomenon of super area law scaling in certain conditions.

Contribution

It introduces a unified framework using linear complex structures to relate bosonic and fermionic Gaussian states and their entanglement spectra in supersymmetric systems.

Findings

Dualities relate von Neumann and Renyi entropies between bosonic and fermionic subsystems.

Super area law scaling of entanglement entropy observed in bosonic systems when dual fermionic modes are highly entangled.

Framework applied to models including the Kitaev honeycomb model.

Abstract

We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both, bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically SUSY preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy ("super area law") in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.