On the Correlation Inequalities in Some Models Involving Fermions

R. Gielerak

Yoshiteru Sato

Roman Gielerak

Abstract Using the Coleman (‐Fröhlich‐Seiler) theorem we have mapped chargeless sectors of some (generalized) Yukawa‐Thirring‐(Schwinger) two‐dimensional models onto pure Bose theories. Discussion of certain correlation inequalities in this framework is made. In particular, we proved that the first and second Griffiths‐Kelly‐Shermann correlation inequalities hold. Correlation inequalities suggest that there is on phase transition of the first order in scalar versions of these models. Some results on the D‐L‐R equations for these models are established, confirming previous suggestion.

H. Kunz, Ch.-Ed. Pfister, Pierre-A. Vuillermot

Leela Ganesh Chandra Lakkaraju, Naga Dileep Varikuti, Philipp Hauke

Interacting fermions owe both their non-trivial correlations and their computational power to their departure from Gaussianity. Yet, quantifying that departure geometrically faces two challenges: the Gaussian manifold is non-convex, and perturbative treatments are confined to weak interactions. Here, we introduce a geometric measure of fermionic non-Gaussianity, the fidelity distance of a target state to the manifold of fermionic Gaussian states. We construct an iteration formalism to numerically access it, applicable also at strong coupling. Further, we prove a sharpened operator Jensen inequality, of interest in its own right. We use it to derive a witness that involves only two- and four-point fermionic correlators. Numerical benchmarks on the one-dimensional Fermi--Hubbard model show that the quality of the witness improves with system size and, for strong coupling, is tighter than antiflatness. Our results open a scalable route to charting non-Gaussianity of strongly-interacting fermionic quantum simulators.

N. Nikitin, K. S. Toms

A relativistic generalization of Bell’s inequalities in Wigner’s form was obtained for the decays of a pseudoscalar and a scalar particle to two particles having a nonzero spin (fermions and photons). Both inequalities involving a full anticorrelation of final-particle spins and having a nonrelativistic analog and inequalities involving a full correlation of spins are considered. It is shown that Bohr’s complementarity principle may be tested experimentally in the relativistic region.