Hilbert-P\'{o}lya conjecture via critical pseudo-magnetic degrees of freedom

Abstract

Motivated by a recent pseudo-spin model for monolayer-bilayer phase transitions in silver-based honeycomb layered materials, we propose that the critical pseudo-magnetic fields in such systems correspond to both the infinite-channel Feshbach resonance widths of a (Fermi-Dirac/Bose-Einstein/etc.) condensate in 2 dimensions, and equivalently to the Lee-Yang zeros of the Ising model of two pseudo-spins with a partition function corresponding to a class of functions that must include the Riemann Xi function. Identifying the quantum-mechanical operator that yields the discontinuous/random/topological spectrum of the critical pseudo-magnetic fields in such systems offers a tenable realisation of the Hilbert-P\'{o}lya conjecture.