Fig. 6: The sign problem for a coupled spin-photon system.
From: Cavity-renormalized quantum criticality in a honeycomb bilayer antiferromagnet
Shown is the parameter space of light matter couplings normalized by system size \(\lambda /\sqrt{N}\) and cavity frequencies Ω normalized by Hubbard repulsion U. Some parameter regions (depending on the photon number cutoff \({n}_{{{{{{{{\rm{ph}}}}}}}}}^{\max }\)) give rise to signful quantum Monte Carlo (QMC) configurations, known as the sign problem. a Exactly sign-free regions according to a sufficient condition based on the matrix elements of the exchange coupling operator \(\langle n| {\hat{{{{{{{{\mathcal{J}}}}}}}}}}_{ij}| m\rangle \ge 0\) for all \(n,m \, < \, {n}_{{{{{{{{\rm{ph}}}}}}}}}^{\max }\). b Actual average sign in a simulation at temperature T = J/2L. For an average sign 〈sign〉 = 1, i.e., outside of the white regions, efficient large-scale simulations are possible. J is the intralayer exchange coupling.
