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Due to the different environments in the Milky Way's disk and halo, comparingwide binaries in the disk and halo is key to understanding wide binaryformation and evolution. By using Gaia Early Data Release 3, we search forresolved wide binary companions in the H3 survey, a spectroscopic survey thathas compiled $\sim$150,000 spectra for thick-disk and halo stars to date. Weidentify 800 high-confidence (a contamination rate of 4%) wide binaries and tworesolved triples, with binary separations mostly between $10^3$-$10^5$ AU and alowest [Fe/H] of $-2.7$. Based on their Galactic kinematics, 33 of them arehalo wide binaries, and most of those are associated with the accretedGaia-Sausage-Enceladus galaxy. The wide binary fraction in the thick diskdecreases toward the low metallicity end, consistent with the previous findingsfor the thin disk. Our key finding is that the halo wide binary fraction isconsistent with the thick-disk stars at a fixed [Fe/H]. There is no significantdependence of the wide binary fraction on the $\alpha$-captured abundance.Therefore, the wide binary fraction is mainly determined by the iron abundance,not their disk or halo origin nor the $\alpha$-captured abundance. Our resultssuggest that the formation environments play a major role for the wide binaryfraction, instead of other processes like radial migration that only apply todisk stars.

Wide binaries from the H3 survey: the thick disk and halo have similar wide binary fractions