Gaussian states, Kähler structures and an entanglement duality

Date: Wednesday, July 6, 2022
Time: 14:15
Location: room 45, ICTQT

Speaker: Robert H. Jonsson (Wallenberg Initiative on Networks and Quantum Information, Nordita (Stockholm)

Abstract Gaussian quantum states play a central role in many branches of physics – from quantum optics, to condensed matter and quantum field theory. In this talk, I aim to showcase the strength of the Kähler structure formalism for Gaussian states by discussing a recent result on the entanglement structure of supersymmetric (SUSY) bosonic and fermionic Gaussian states [1]. Mathematically, Gaussian states can be defined in terms of Kähler structures on classical phase space. In fact, this approach has proven to be very powerful: It yields a formalism which is both practical for applications, clearly captures the structure and geometry of Gaussian states, adapts to discrete and continuous settings and, moreover, can treat bosons and fermions simultaneously. To exemplify this, we will consider the basic example of a free SUSY system. This is a pair of one bosonic and one fermionic quadratic hamiltonian which is generated by a supercharge and, therefore, is isospectral. Not only does the Kähler structure formalism parallelly capture the Gaussian ground states and their entanglement structure of both the bosonic and the fermionic part. Moreover, it allows us to derive an appealing entanglement duality between bosonic and fermionic subsystems [1], and to interpret it in terms of phase space geometry and its physical implications. Time permitting, as a special application, we consider topological insulators and superconductors and their SUSY partners, discussing the recently derived classification of supercharges in this context [2]. [1] Jonsson, Robert H., Lucas Hackl, and Krishanu Roychowdhury. “Entanglement Dualities in Supersymmetry.” Physical Review Research 3, no. 2 (June 16, 2021): 023213. [2] Gong, Zongping, Robert H. Jonsson, and Daniel Malz. “Supersymmetric Free Fermions and Bosons: Locality, Symmetry, and Topology.” Physical Review B 105, no. 8 (February 24, 2022): 085423.