Bosonic and fermionic systems that are identified by supersymmetry (SUSY) display identical features beyond single-particle band structures, such as band topology. In this talk, I will extend this identification to capture features of entanglement in the Gaussian states, which are the ground states of supersymmetric quadratic Hamiltonians, by deriving a general relation between the bosonic and fermionic entanglement. The derivation relies on a unified framework to describe both bosonic and fermionic Gaussian states in terms of so-called linear complex structures on a Kähler manifold. 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 of the respective subsystems can be related. I will illustrate the findings in one- and two-dimensional systems, including the paradigmatic Kitaev chain and the honeycomb model. While typically supersymmetry preserves features like area law scaling of the entanglement entropies on either side, a peculiar phenomenon draws attention, namely, an amplified scaling of the entanglement entropy (“super area law”) in bosonic subsystems whilst the dual fermionic subsystems develop almost maximally entangled modes.
Meeting ID: 869 2900 8797